Oscillations

The x-t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t = 2 s is : [figure]

1. - 28 m s-2
2. 216 m s-2
3. - 216 m s-2
4. 28 m s-2

Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :

1. 11
2. 9
3. 10
4. 8

Match List-I with List-II Choose the correct answer from the options given below

1. (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
2. (a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)
3. (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
4. (a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)

The restoring force of a spring with a block attached to the free end of the spring is represented by

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Identify the function which represents a non-periodic motion.

1. ( t + /4)
2. e- t
3. t
4. t + t

A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is :

1. 4n
2. n
3. 2n
4. 3n

A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is -

1. 0.628 s
2. 0.0628 s
3. 6.28 s
4. 3.14 s

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :

1. 3 2 rad
2. 2 rad
3. zero
4. rad

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. [figure] y- projection of the radius vector of rotating particle P is :

1. y(t) = 4 ( t2 ), where y in m
2. y(t) = 3 ( 3 t2 ), where y in m
3. y(t) = 3 ( t2 ), where y in m
4. y(t) = -3 2 t, where y in m

Average velocity of a particle executing SHM in one complete vibration is :

1. A
2. A 22
3. A 2
4. zero