## MCQ (Single Correct Answer)

In a linear Simple Harmonic Motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement ar...

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :...

Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position ?...

A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half o...

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $$(x)$$ starting from mean position to extre...

A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is $$x=\frac{A}{2}$$ and it moves along positive x-axis...

For particle P revolving round the centre O with radius of circular path $$\mathrm{r}$$ and angular velocity $$\omega$$, as shown in below figure, the...

A mass $$m$$ is attached to two strings as shown in figure. The spring constants of two springs are $$\mathrm{K}_{1}$$ and $$\mathrm{K}_{2}$$. For the...

Choose the correct length (L) versus square of the time period ($$\mathrm{T}^{2}$$) graph for a simple pendulum executing simple harmonic motion....

The maximum potential energy of a block executing simple harmonic motion is $$25 \mathrm{~J}$$. A is amplitude of oscillation. At $$\mathrm{A / 2}$$, ...

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1 \mathrm{~kg}$, the angular f...

A particle executes simple harmonic motion between $$x=-A$$ and $$x=+A$$. If time taken by particle to go from $$x=0$$ to $$\frac{A}{2}$$ is 2 s; then...

T is the time period of simple pendulum on the earth's surface. Its time period becomes $$x$$ T when taken to a height R (equal to earth's radius) abo...

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined pl...

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height...

When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :

In figure $$(\mathrm{A})$$, mass '$$2 \mathrm{~m}^{\text {' }}$$ is fixed on mass '$$\mathrm{m}$$ ' which is attached to two springs of spring consta...

The motion of a simple pendulum executing S.H.M. is represented by the following equation.
$$y = A\sin (\pi t + \phi )$$, where time is measured in se...

Motion of a particle in x-y plane is described by a set of following equations $$x = 4\sin \left( {{\pi \over 2} - \omega t} \right)\,m$$ and $$y = 4...

The equation of a particle executing simple harmonic motion is given by $$x = \sin \pi \left( {t + {1 \over 3}} \right)m$$. At t = 1s, the speed of pa...

The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of h...

Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $${g \over 6}$$ vertically upwards then the time period wil...

Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such tha...

A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A sim...

A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that...

For a body executing S.H.M. :(1) Potential energy is always equal to its K.E.(2) Average potential and kinetic energy over any given time interval are...

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.The potential energy U(x) versus ti...

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of ...

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $${{3E} \over 4}$$...

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean ...

T0 is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to $${1 \over {16}}$$ times of its initial value, the ...

A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1...

The function of time representing a simple harmonic motion with a period of $${\pi \over \omega }$$ is :

The time period of a simple pendulum is given by $$T = 2\pi \sqrt {{l \over g}} $$. The measured value of the length of pendulum is 10 cm known to a 1...

Two particles A and B of equal masses are suspended from two massless springs of spring constants K1 and K2 respectively. If the maximum velocities du...

A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm. After 2 minutes the amplitude decreases to 6 cm. De...

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how muc...

Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period o...

A particle executes S.H.M., the graph of velocity as a function of displacement is :

Given below are two statements :Statement I : A second's pendulum has a time period of 1 second.Statement II : It takes precisely one second to move b...

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Eart...

If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor :...

Y = A sin($$\omega$$t + $$\phi$$0) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is $$Y = {A \over 2}$$ and it...

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equ...

The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30$$^\circ$$ in 0.1 s. The perpendicular projec...

If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :

In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to f...

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}} $$. Measured value of 'L' is 1.0 m from meter scale having a minimum ...

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k...

When a particle of mass m is attached to a vertical spring of spring constant k and released, its
motion is described by y(t) = y0
sin2 $$\omega $$t, ...

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on
a frictionless horizontal plane. If half of the m...

The displacement time graph of a particle
executing S.H.M is given in figure :(sketch is
schematic and not to scale)
Which of the following statement...

A spring mass system (mass m, spring
constant k and natural length $$l$$) rest in
equilibrium on a horizontal disc. The free end
of the spring is fixe...

A simple pendulum is being used to determine
th value of gravitational acceleration g at a
certain place. Th length of the pendulum is
25.0 cm and a s...

The displacement of a damped harmonic
oscillator is given by
x(t ) = e–0.1t cos (10$$\pi $$t + f). Here t is in seconds.
The time taken for its amplit...

A damped harmonic oscillator has a frequency
of 5 oscillations per second. The amplitude
drops to half its value for every 10 oscillations.
The time i...

A simple harmonic motion is represented by :
y = 5 (sin 3 $$\pi $$ t + $$\sqrt 3 $$ cos 3 $$\pi $$t) cm
The amplitude and time period of the motion ar...

Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length $$\ell $$ and mass...

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a s...

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of simple pendulum on the Earth i...

A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple h...

A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin$${{\pi t} \over {90}}$$. The ratio of kinetic to pot...

A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will...

A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward sligh...

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its veloci...

A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic ener...

A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at ...

An oscillator of mass M is at rest in its equilibrium position in a potential
V = $${1 \over 2}$$ k(x $$-$$ X)2. A particle of mass m comes from rig...

A particle executes simple harmonic motion and is located at x = a, b and c at times t0, 2t0 and 3t0 respectively. The freqquency of the oscillation ...

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds ...

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
x(t) = A sin (at + $$\delta $$)
y(t) =...

A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm−1 and oscillates in a damping medium of damping constant 10−2 kg s...

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring a...

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1 . At, t = 0 the displacement is 5 m. What is the maximum a...

A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of
equilibrium. The kinetic energy – time gr...

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The moto...

Two particles are performing simple harmonic motion in a straight line about
the same equilibrium point. The amplitude and time period for both partic...

A particle performs simple harmonic motion with amplitude $$A.$$ Its speed is trebled at the instant that it is at a distance $${{2A} \over 3}$$ from ...

The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}} $$. Measured value of L is 20.0 cm known to 1 mm accuracy and time f...

A pendulum made of a uniform wire of cross sectional area $$A$$ has time period $$T.$$ When an additional mass $$M$$ is added to its bob, the time per...

For a simple pendulum, a graph is plotted between its kinetic energy $$(KE)$$ and potential energy $$(PE)$$ against its displacement $$d.$$ Which one ...

A particle moves with simple harmonic motion in a straight line. In first $$\tau s,$$ after starting from rest it travels a distance $$a,$$ and in nex...

The amplitude of a damped oscillator decreases to $$0.9$$ times its original magnitude in $$5s$$. In another $$10s$$ it will decrease to $$\alpha $$ ...

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and the cylinder have equal cross ...

If a simple pendulum has significant amplitude (up to a factor of $$1/e$$ of original ) only in the period between $$t = 0s\,\,to\,\,t = \tau \,s,$$ t...

Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega $$ along the $$x$$-axis. Their mean position is ...

A mass $$M,$$ attached to a horizontal spring, executes $$S.H.M.$$ with amplitude $${A_1}.$$ When the mass $$M$$ passes through its mean position then...

If $$x,$$ $$v$$ and $$a$$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $$T...

Two springs, of force constant $${k_1}$$ and $${k_2}$$ are connected to a mass $$m$$ as shown. The frequency of oscillation of the mass is $$f.$$ If b...

A particle of mass $$m$$ executes simple harmonic motion with amplitude a and frequency $$v.$$ The average kinetic energy during its motion from the p...

A point mass oscillates along the $$x$$-axis according to the law $$x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).$$ If the acceleration of the p...

The displacement of an object attached to a spring and executing simple harmonic motion is given by $$x = 2 \times {10^{ - 2}}$$ $$cos$$ $$\pi t$$ met...

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega .$$ The amplitude of oscillati...

Starting from the origin a body oscillates simple harmonically with a period of $$2$$ $$s.$$ After what time will its kinetic energy be $$75\% $$ of t...

The maximum velocity of a particle, executing simple harmonic motion with an amplitude $$7$$ $$mm,$$ is $$4.4$$ $$m/s.$$ The period of oscillation is

The function $${\sin ^2}\left( {\omega t} \right)$$ represents

Two simple harmonic motions are represented by the equations $${y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \right)$$ and $${y_2} = 0.1\,\cos ...

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugg...

If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is

The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillation of the bob is $${t_0}$$ in ...

The total energy of particle, executing simple harmonic motion is

A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another spring is $${t_2}$$. If the p...

A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omega _0}.$$ An external force $$F...

In forced oscillation of a particle the amplitude is maximum for a frequency $${\omega _1}$$ of the force while the energy is maximum for a frequency ...

A mass $$M$$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $$SHM$$ of time ...

Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k_1}$$ and $${k_2}$$, respectiv...

The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in the time period of the pendulum...

A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kinetic energy $$(K.E)$$ and total energy $$(T.E)$$ are measured as a func...

The displacement of particle varies according to the relation
$$x=4$$$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$$ The amplitude of the particle ...

If a spring has time period $$T,$$ and is cut into $$n$$ equal parts, then the time period of each part will be

In a simple harmonic oscillator, at the mean position

A child swinging on a swing in sitting position, stands up, then the time period of the swing will

## Numerical

At a given point of time the value of displacement of a simple harmonic oscillator is given as $$\mathrm{y}=\mathrm{A} \cos \left(30^{\circ}\right)$$....

A rectangular block of mass $$5 \mathrm{~kg}$$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $$1 \mathrm{~m}$$ a...

A simple pendulum with length $$100 \mathrm{~cm}$$ and bob of mass $$250 \mathrm{~g}$$ is executing S.H.M. of amplitude $$10 \mathrm{~cm}$$. The maxim...

The amplitude of a particle executing SHM is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be $$25 \%$$ more than the potentia...

In the figure given below, a block of mass $$M=490 \mathrm{~g}$$ placed on a frictionless table is connected with two springs having same spring const...

The velocity of a particle executing SHM varies with displacement $(x)$ as $4 v^{2}=50-x^{2}$. The time period of oscillations is $\frac{x}{7} s$. The...

The general displacement of a simple harmonic oscillator is $$x = A\sin \omega t$$. Let T be its time period. The slope of its potential energy (U) - ...

A particle of mass 250 g executes a simple harmonic motion under a periodic force $$\mathrm{F}=(-25~x)\mathrm{N}$$. The particle attains a maximum spe...

A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases b...

A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the e...

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $$10 \mathrm{~s}$$. If the metallic bob is immerse...

The potential energy of a particle of mass $$4 \mathrm{~kg}$$ in motion along the x-axis is given by $$\mathrm{U}=4(1-\cos 4 x)$$ J. The time period o...

A mass $$0.9 \mathrm{~kg}$$, attached to a horizontal spring, executes SHM with an amplitude $$\mathrm{A}_{1}$$. When this mass passes through its mea...

As per given figures, two springs of spring constants $$k$$ and $$2 k$$ are connected to mass $$m$$. If the period of oscillation in figure (a) is $$3...

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean posi...

A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60$...

A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum...

A particle of mass 1 kg is hanging from a spring of force constant 100 Nm$$-$$1. The mass is pulled slightly downward and released so that it executes...

Two simple harmonic motion, are represented by the equations $${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$$ $${y_2} = 5(\sin 3\pi t + \sq...

Two simple harmonic motions are represented by the equations $${x_1} = 5\sin \left( {2\pi t + {\pi \over 4}} \right)$$ and $${x_2} = 5\sqrt 2 (\sin 2...

A particle executes simple harmonic motion represented by displacement function as x(t) = A sin($$\omega$$t + $$\phi$$)If the position and velocity of...

In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position...

A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60$$^\circ...

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its ampl...

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 show...

A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is $${{\s...

Time period of a simple pendulum is T. The time taken to complete $${5 \over 8}$$ oscillations starting from mean position is $${\alpha \over \beta }...