Oscillations

The frequency of oscillation of a mass m suspended by a spring is 1. If the length of the spring is cut to half, the same mass oscillates with frequency 2. The value of 2 1 is .

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

A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x=A to x= A 2 is sec.

1. 1/4
2. 5/4
3. 5/8
4. 3/8

A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are Hz and J, respectively. (Take g = 10 m/s2)

1. 5 50 and 8 10-3
2. 5 50 and 8
3. 10 50 and 2 10-3
4. 5 50 and 16 10-3

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

1. A-III, B-I, C-IV, D-II
2. A-II, B-I, C-III, D-IV
3. A-III, B-II, C-IV, D-I
4. A-II, B-I, C-IV, D-III

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