Oscillations

The velocity of a particle executing simple harmonic motion along x-axis is described as v2=50-x2, where x represents displacement. If the time period of motion is x7 s, the value of x is .

A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is . (g is acceleration due to gravity) [figure]

1. 2 5R4g
2. 2 2R3g
3. 2 3R2g
4. 2 3Rg

The equation of motion of a particle is given by x=a (50t+ /3) cm. The particle will come to rest at time t1 and it will have zero acceleration at time t2. The t1 and t2 respectively are .

1. 300 s, 75 s
2. 75 s, 300 s
3. 300 s, 25 s
4. 50 s, 100 s

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