Question

A block of mass m is connected to a spring constant k and is at rest in equilibrium as shown. Now, the block is Displacement by h below its equilibrium position and imparted a speed `v_0` towards down as shown in the Fig. As a result of the jerk, the block executes simple harmonic motion about its equilibrium position. Based on this information, answer the following question.
Q. Find the time taken by the block to cross the mean position for the first time.
A. `(2pi-cos^-1((h)/(A)))/(sqrt((k)/(m)))`
B. `((pi)/(2)-cos^-1((h)/(A)))/(sqrt((k)/(m)))`
C. `(pi-sin^-1((h)/(A)))/(sqrt((k)/(m)))`
D. `(pi-sin^-1((h)/(A)))/(2sqrt((k)/(m)))`

Answer 1

Correct Answer - C
To compute the time taken by the block to cross mean position for the first time, we can make use of circular motion representation.
`t=(pi-delta)/(omega)=(pi-sin^-1((h)/(A)))/(sqrt((k)/(m)))`