## Numerical

A particle of mass $1 \mathrm{~kg}$ is subjected to a force which depends on the position as $\vec{F}=$ $-k(x \hat{\imath}+y \hat{\jmath}) \mathrm{kg}...

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its crosssectional area is 4.9 $$ \times $$ 10-7 m2. If t...

## MCQ (More than One Correct Answer)

A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. Th...

Two independent harmonic oscillators of equal masses are oscillating about the origin with angular frequencies $$\omega$$1 and $$\omega$$2 and have to...

## MCQ (Single Correct Answer)

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The sy...

The phase space diagram for a ball thrown vertically up from ground is

The phase space diagram for simple harmonic motion is a circle centred at the origin. In the figure, the two circles represent the same oscillator but...

Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is
...

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $${x_1}\left( t \right) = A\sin \omega t$$ and $${x_2}\left( t ...

A wooden block performs $$SHM$$ on a frictionless surface with frequency, $${v_0}.$$ The block carries a charge $$+Q$$ on its surface . If now a unif...

If the total energy of the particle is E, it will perform periodic motion only if

For periodic motion of small amplitude A, the time period T of this particle is proportional to

The acceleration of this particle for $$|x| > {X_0}$$ is

A simple pendulum has time period T1. The point of suspension is now moved upward according to the relation y = Kt2, (K = 1 m/s2) where y is the verti...

A particle executes simple harmonic motion between x = - A to x = + A. The time taken for it to go from 0 to $${A \over 2}$$ is T1 and to go from $${A...

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

A particle free to move along the x-axis has potential energy given by $$U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]$$ fo...

Two bodies M and N of equal masses are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the two bodies oscil...

## Fill in the Blanks

An object of mass 0.2 kg executes simple harmonic oscillation along the x-axis with a frequency of $$\left( {{{25} \over \pi }} \right)$$ Hz. At the p...