If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period becomes :

• 3 T

• 3/2T

• 4T

• 2T

A pendulum is undergoing SHM with frequency f What is the frequency of its kinetic energy ?

• $\frac{\mathrm{f}}{2}$

• 2 f

• 3 f

• 4 f

Two equal -ve charges -q are fixed at the point (O, a) and (O, a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge will :

• execute SHM about the origin

• move to the origin and remain at rest

• move to infinity

• execute oscillatory but not SHM

The circular motion of a particle with constant speed is

• simple harmonic but not periodic

• periodic and simple harmonic

• neither periodic nor simple harmonic

• periodic but not simple harmonic

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

• 3 Hz

• 2 Hz

• 4 Hz

• 1 Hz

A particle executes simple harmonic oscillation with an amplitude $\mathrm{\alpha }$ . The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

• $\frac{\mathrm{T}}{4}$

• $\frac{\mathrm{T}}{8}$

• $\frac{\mathrm{T}}{12}$

• $\frac{\mathrm{T}}{2}$

Given that $\mathrm{y} = \mathrm{A} \sin \left[\left( \frac{2\mathrm{\pi }}{\mathrm{\lambda }} \left(\mathrm{ct} - \mathrm{x}\right) \right)\right]$ , where y and x are measured in metre. Which of the following statements is true?

• The unit of λ is same as that of x and A

• The unit of λ is same as that of x but not of A

• The unit of c is same as that of $\frac{2\mathrm{\pi }}{\mathrm{\lambda }}$

• The unit of ( ct - x ) is same as that of $\frac{2\mathrm{\pi }}{\mathrm{\lambda }}$

Two simple pendulums of length 0.5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has
completed x oscillations, where k is

• 1

• 3

• 2

• 5

A mass of 1 kg is suspended from a spring of force constant 400 N, executing SHM total energy of the body is 2J, then maximum acceleration of the spring will be

• 4 m/s²

• 40 m/s²

• 200 m/s²

• 400 m/s²

Vibrations of rope tied by two rigid ends shown by equation y = cos 2πt sin2πx, then minimum length of the rope will be

• 1 m

• $\frac{1}{2}\mathrm{m}$

• 5 m

• 2πm