# NCERT Physics Class 11 Exemplar Ch 14 Oscillations Part 4

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## SA

29. Find the time period of mass M when displaced from its equilibrium positon and then released for the system shown in Fig 10.

Ans: If mass m moves down by h, then the spring extends by 2h (because each side expands by h). The tension along the string and spring is the same.

In equilibrium

Where k is the spring constant. On pulling the mass down by x,

So.

30. Show that the motion of a particle represented byis simple harmonic with a period of.

Ans:

31. Find the displacement of a simple harmonic oscillator at which its P.E. is half of the maximum energy of the oscillator.

Ans:

32. A body of mass m is situated in a potential field when and are constants. Find the time period of small oscillations.

Ans:

We know that

So.

33. A mass of 2 kg is attached to the spring of spring constant. The block is pulled to a distance of 5cm from its equilibrium position at on a horizontal frictionless surface from rest at. Write the expression for its displacement at any time t.

Ans:.

34. Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of to the right with the vertical, the other pendulum makes an angle of to the left of the vertical. What is the phase difference between the pendulums?

Ans:

For the first,

For the 2^{nd},