Oscillations

The displacement of a particle, executing simple harmonic motion with time period T, is expressed as x(t) = A t, where A is the amplitude. The maximum value of potential energy of this oscillator is found at t = T/2 . The value of is .

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is : [figure]

1. 20
2. 5
3. 30
4. 27

A cylindrical block of mass M and area of cross section A is floating in a liquid of density and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is

1. 2 AMg
2. 2M Ag
3. 2 M Ag
4. AMg

A spring of force constant 15 N/m is cut into two pieces. If the ratio of their lengths is 1 : 3, then the force constant of smaller piece is N/m.

1. 20
2. 45
3. 60
4. 15

A simple pendulum of string length 30 cm performs 20 oscillations in 10 s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is cm. [Assume that the mass of the pendulum remains same.]

1. 0.75
2. 7.5
3. 15
4. 120

Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T ?

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

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad/s. The frequency of this simple harmonic oscillator is Hz. [take = 227]

1. 88
2. 14
3. 28
4. 176

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be

1. 10 [1 - (2 - x)2 ] 12 m/s
2. 10 [1 - (2 - x)2 ] 32 m/s
3. 10 [1 - (2 - x)2 ] m/s
4. 10 [1 - (2 - x)2 ]2 m/s

Two simple pendulums having lengths l1 and l2 with negligible string mass undergo angular displacements 1 and 2, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

1. 1 l2 = 2 l1
2. 1 l1 = 2 l2
3. 1 l22 = 2 l12
4. 1 l12 = 2 l22

[figure] Two blocks of masses m and M, (M > m), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( = coefficient of friction between the two blocks) Choose the correct answer from the options given below :

1. B, C, D Only
2. C, D, E Only
3. A, B, D Only
4. A, B, C Only