Oscillations

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

A particle is subjected to two simple harmonic motions as : x1 = 7 5t cm and x2 = 2 7 (5t + 3 )cm where x is displacement and t is time in seconds. The maximum acceleration of the particle is x 10-2 m s-2. The value of x is :

1. 5 7
2. 125
3. 25 7
4. 175

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both (A) and (R) are true but (R) is not the correct explanation of (A).
2. (A) is true but (R) is false.
3. Both (A) and (R) are true and (R) is the correct explanation of (A).
4. (A) is false but (R) is true.

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

1. k2k1
2. k1k2
3. k2k1
4. k1k2

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

1. (A) is true but (R) is false
2. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
3. (A) is false but (R) is true
4. Both (A) and (R) are true and (R) is the correct explanation of (A)

A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm. If D and d are the total distance and displacement covered by the particle in 12.5 s, then Dd is

1. 10
2. 165
3. 25
4. 154

A particle oscillates along the x-axis according to the law, x(t)=x0 2 ( t2 ) where x0=1 m. The kinetic energy (K) of the particle as a function of x is correctly represented by the graph

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

A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is y 10-2 s, where the value of y is (Acceleration due to gravity, g=10 m/s2, density of water =103 kg/m3 )

1. 2
2. 4
3. 1
4. 6