Simple Harmonic Motion · Physics · MHT CET
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MHT CET 2023 14th May Evening Shift
A uniform circular disc of mass $$12 \mathrm{~kg}$$ is held by two identical springs. When the disc is slightly pressed down and released, it executes...
MHT CET 2023 14th May Evening Shift
A light spring is suspended with mass $$m_1$$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance an...
MHT CET 2023 14th May Evening Shift
A block of mass '$$M$$' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the...
MHT CET 2023 14th May Morning Shift
A simple pendulum of length '$$l$$' and a bob of mass '$$\mathrm{m}$$' is executing S.H.M. of small amplitude '$$A$$'. The maximum tension in the stri...
MHT CET 2023 14th May Morning Shift
The displacement of a particle executing S.H.M. is $$x=\mathrm{a} \sin (\omega t-\phi)$$. Velocity of the particle at time $$\mathrm{t}=\frac{\phi}{\o...
MHT CET 2023 14th May Morning Shift
The bob of simple pendulum of length '$$L$$' is released from a position of small angular displacement $$\theta$$. Its linear displacement at time '$$...
MHT CET 2023 13th May Evening Shift
Under the influence of force $$F_1$$ the body oscillates with a period $$T_1$$ and due to another force $$F_2$$ body oscillates with period $$T_2$$. I...
MHT CET 2023 13th May Evening Shift
A mass $$M$$ is suspended from a light spring. An additional mass $$M_1$$ added extends the spring further by a distance $$x$$. Now, the combined mass...
MHT CET 2023 13th May Morning Shift
A body of mass $$0.04 \mathrm{~kg}$$ executes simple harmonic motion (SHM) about $$\mathrm{x}=0$$ under the influence of force $$\mathrm{F}$$ as shown...
MHT CET 2023 13th May Morning Shift
A simple pendulum has a time period '$$T$$' in air. Its time period when it is completely immersed in a liquid of density one eighth the density of th...
MHT CET 2023 12th May Evening Shift
In a stationary lift, time period of a simple pendulum is '$$\mathrm{T}$$'. The lift starts accelerating downwards with acceleration $$\left(\frac{\ma...
MHT CET 2023 12th May Evening Shift
A particle starts from mean position and performs S.H.M. with period 4 second. At what time its kinetic energy is $$50 \%$$ of total energy?
$$\left(\...
MHT CET 2023 12th May Morning Shift
A simple pendulum performs simple harmonic motion about $$\mathrm{x}=0$$ with an amplitude '$$\mathrm{a}$$' and time period '$$T$$'. The speed of the ...
MHT CET 2023 12th May Morning Shift
Four massless springs whose force constants are $$2 \mathrm{~K}, 2 \mathrm{~K}, \mathrm{~K}$$ and $$2 \mathrm{~K}$$ respectively are attached to a mas...
MHT CET 2023 11th May Evening Shift
The upper end of the spring is fixed and a mass '$$m$$' is attached to its lower end. When mass is slightly pulled down and released, it oscillates wi...
MHT CET 2023 11th May Morning Shift
For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$$x$$' from the mean position. If '$$A$$'...
MHT CET 2023 11th May Morning Shift
The time period of a simple pendulum inside a stationary lift is '$$T$$'. When the lift starts accelerating upwards with an acceleration $$\left(\frac...
MHT CET 2023 10th May Evening Shift
A body is executing a linear S.H.M. Its potential energies at the displacement '$$\mathrm{x}$$' and '$$\mathrm{y}$$' are '$$\mathrm{E}_1$$' and '$$E_2...
MHT CET 2023 10th May Evening Shift
A simple harmonic progressive wave is represented by $$y=A \sin (100 \pi t+3 x)$$. The distance between two points on the wave at a phase difference o...
MHT CET 2023 10th May Morning Shift
The amplitude of a particle executing S.H.M. is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be $$25 \%$$ more than the poten...
MHT CET 2023 9th May Evening Shift
Two S.H.Ms. are represented by equations $$\mathrm{y}_1=0.1 \sin \left(100 \pi \mathrm{t}+\frac{\pi}{3}\right)$$ and $$\mathrm{y}_2=0.1 \cos (100 \pi ...
MHT CET 2023 9th May Evening Shift
A spring has a certain mass suspended from it and its period for vertical oscillations is '$$T_1$$'. The spring is now cut in to two equal halves and ...
MHT CET 2023 9th May Evening Shift
A particle is vibrating in S.H.M. with an amplitude of $$4 \mathrm{~cm}$$. At what displacement from the equilibrium position is its energy half poten...
MHT CET 2023 9th May Morning Shift
A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum
MHT CET 2023 9th May Morning Shift
The maximum velocity of a particle performing S.H.M. is '$$\mathrm{V}$$'. If the periodic time is made $$\left(\frac{1}{3}\right)^d$$ and the amplitud...
MHT CET 2022 11th August Evening Shift
The time taken by a particle executing simple harmonic motion of period '$$\mathrm{T}$$', to move from the mean position to half the maximum displacem...
MHT CET 2022 11th August Evening Shift
In a medium, the phase difference between two particles separated by a distance '$$x$$' is $$\left(\frac{\pi}{5}\right)^{\text {c }}$$. If the frequen...
MHT CET 2022 11th August Evening Shift
A particle starts oscillating simple harmonically from its mean position with time period '$$T$$'. At time $$t=\frac{T}{12}$$, the ratio of the potent...
MHT CET 2021 24th September Evening Shift
The displacement of a particle performing S.H.M. is given by $$x=5 \sin (3 t+3)$$, where $$x$$ is in $$\mathrm{cm}$$ and $$t$$ is in second. The maxim...
MHT CET 2021 24th September Morning Shift
Two identical springs of constant '$$\mathrm{K}$$' are connected in series and parallel in shown in figure. A mass '$$\mathrm{M}$$' is suspended from ...
MHT CET 2021 24th September Morning Shift
A particle performing linear S.H.M. of amplitude $$0.1 \mathrm{~m}$$ has displacement $$0.02 \mathrm{~m}$$ and acceleration $$0.5 \mathrm{~m} / \mathr...
MHT CET 2021 24th September Morning Shift
A body is executing S.H.M. under the action of force having maximum magntude $$50 \mathrm{~N}$$. When its energy is half kinetic and half potential; t...
MHT CET 2021 23rd September Evening Shift
A bob of simple pendulum of mass 'm' perform $$\mathrm{SHM}$$ with amplitude '$$\mathrm{A}$$' and period 'T'. Kinetic energy of pendulum of displaceme...
MHT CET 2021 23rd September Evening Shift
An object executes SHM along $$x$$-axis with amplitude $$0.06 \mathrm{~m}$$. At certain distance '$$\mathrm{x}$$' metre from mean position, it has kin...
MHT CET 2021 23rd September Evening Shift
A body executes SHM under the action of force '$$\mathrm{F}_1$$' with time period '$$\mathrm{T}_1$$'. If the force is changed to '$$\mathrm{F_2}$$', i...
MHT CET 2021 23th September Morning Shift
A particle performing S.H.M. when displacement is '$$x$$', the potential energy and restoring force acting on it are denoted by '$$E$$' and '$$F$$' re...
MHT CET 2021 23th September Morning Shift
A body is performing S.H.M. of amplitude 'A'. The displacement of the body from a point where kinetic energy is maximum to a point where potential ene...
MHT CET 2021 23th September Morning Shift
A particle excuting S.H.M starts from the mean position. Its amplitude is 'A' and time period '$$\mathrm{T}$$' At what displacement its speed is one-f...
MHT CET 2021 22th September Evening Shift
A particle connected to the end of a spring executes S.H.M. with period '$$T_1$$'. While the corresponding period for another spring is '$$\mathrm{T}_...
MHT CET 2021 22th September Evening Shift
'$$n$$' waves are produced on a string in 1 second. When the radius of the string is doubled, keeping tension same, the number of waves produced in 1 ...
MHT CET 2021 22th September Evening Shift
A body of mass '$$m$$' performs linear S.H.M. given by equation $$x=P \sin \omega t+Q \sin \left(\omega t+\frac{\pi}{2}\right)$$. The total energy of ...
MHT CET 2021 22th September Morning Shift
A mass $$0.4 \mathrm{~kg}$$ performs S.H.M. with a frequency $$\frac{16}{\pi} \mathrm{Hz}$$. At a certain displacement it has kinetic energy $$2 \math...
MHT CET 2021 22th September Morning Shift
If the amplitude of linear S.H.M. is decreased then
MHT CET 2021 21th September Evening Shift
A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground $$0.75 \mathrm{~cm}$$ and $$2 \mathrm{~m}$$ respect...
MHT CET 2021 21th September Evening Shift
A pendulum clock is running fast. To correct its time, we should
MHT CET 2021 21th September Evening Shift
A particle is performing S.H.M. with maximum velocity '$$v$$'. If the amplitude is tripled and periodic time is doubled then maximum velocity will be...
MHT CET 2021 20th September Evening Shift
A particle executes S.H.M. of period $$\frac{2 \pi}{\sqrt{3}}$$ second along a straight line $$4 \mathrm{~cm}$$ long. The displacement of the particle...
MHT CET 2021 20th September Evening Shift
A particle is suspended from a vertical spring which is executing S.H.M. of frequency $$5 \mathrm{~Hz}$$. The spring is unstretched at the highest poi...
MHT CET 2021 20th September Evening Shift
A body performs S.H.M. under the action of force '$$\mathrm{F}_1$$' with period '$$\mathrm{T}_1$$' second. If the force is changed to '$$\mathrm{F}_2$...
MHT CET 2021 20th September Morning Shift
A mass '$$\mathrm{m}_1$$' is suspended from a spring of negligible mass. A spring is pulled slightly in downward direction and released, mass performs...
MHT CET 2021 20th September Morning Shift
Two particles $$\mathrm{P}$$ and $$\mathrm{Q}$$ performs S.H.M. of same amplitude and frequency along the same straight line. At a particular instant,...
MHT CET 2021 20th September Morning Shift
A particle of mass 5kg is executing S.H.M. with an amplitude 0.3 m and time period $$\frac{\pi}{5}$$s. The maximum value of the force acting on the pa...
MHT CET 2020 19th October Evening Shift
Two bodies $A$ and $B$ of equal mass are suspended from two separate massles springs of force constant $k_1$ and $k_2$, respectively. The bodies oscil...
MHT CET 2020 19th October Evening Shift
A bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$, then the maximum tension in th...
MHT CET 2020 19th October Evening Shift
A body of mass 64 g is made to oscillate turn by turn on two different springs $A$ and $B$. Spring $A$ and $B$ has force constant $4 \frac{\mathrm{~N}...
MHT CET 2020 16th October Evening Shift
The damping force of an oscillator is directly proportional to the velocity. The unit of constant of proportionality is
MHT CET 2020 16th October Evening Shift
A particle performs simple harmonic motion with period of 3 s . The time taken by it to cover a distance equal to half the amplitude from mean positio...
MHT CET 2020 16th October Evening Shift
A simple pendulum of length $$I$$ has a bob of mass $$m$$. It executes SHM of small amplitude A. The maximum tension in the string is ($$g=$$ accelera...
MHT CET 2020 16th October Evening Shift
A block of mass $$m$$ attached to one end of the vertical spring produces extension $$x$$. If the block is pulled and released, the periodic time of o...
MHT CET 2020 16th October Morning Shift
A simple pendulum of length $$L$$ has mass $$m$$ and it oscillates freely with amplitude $$A$$. At extreme position, its potential energy is ($$g=$$ a...
MHT CET 2020 16th October Morning Shift
For a particle performing SHM when displacement is $$x$$, the potential energy and restoring force acting on it is denoted by $$E$$ and $$F$$, respect...
MHT CET 2019 2nd May Evening Shift
A particle is performing a linear simple harmonic motion of amplitude ' $A$ '. When it is midway between its mean and extreme position, the magnitudes...
MHT CET 2019 2nd May Evening Shift
Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of t...
MHT CET 2019 2nd May Evening Shift
If ' $x$ ', $v$ ' and ' $a$ ' denote the displacement, velocity and acceleration of a particle respectively executing SHM of periodic time $h$ then wh...
MHT CET 2019 2nd May Morning Shift
The quantity which does not vary periodically for a particle performing SHM is
MHT CET 2019 2nd May Morning Shift
A particle executes the simple harmonic motion with an amplitude ' $A$ '. The distance travelled by it in one periodic time is