Oscillations

If x = 5 ( t + 3 ) m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

1. 5 cm, 2 s
2. 5 m, 2 s
3. 5 cm, 1 s
4. 5 m, 1 s

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x2 times its original time period. Then the value of x is:

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

A particle executing simple harmonic motion with amplitude A has the same potential and kinetic energies at the displacement

1. 2 A
2. A2
3. A 2
4. A 2

The two-dimensional motion of a particle, described by r = ( i + 2 j)A t is a/an: Choose the correct answer from the options given below:

1. B, C and D only
2. A, B and C only
3. A, C and D only
4. C and D only

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