A block of mass \( m \) is connected to a spring of spring constant \( k \) and is at rest in eq...

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A block of mass \( m \) is connected to a spring of spring constant \( k \) and is at rest in equilibrium as shown. Now, the block is displaced by \( h \) below its equilibrium position and imparted a speed \( v_{0} \) towards down as shown in the given figure.

As a result of the jerk, the block executes simple harmonic motion about its equilibrium position. Based on this information, answer the following questions:

Find the time taken by the block to cross the mean position for the first time.
(1) \( \frac{2 \pi-\cos ^{-1}\left(\frac{h}{A}\right)}{\sqrt{\frac{k}{m}}} \)
(2) \( \frac{\frac{\pi}{2}-\cos ^{-1}\left(\frac{h}{A}\right)}{\sqrt{\frac{k}{m}}} \)
3) \( \frac{\pi-\sin ^{-1}\left(\frac{h}{A}\right)}{\sqrt{\frac{k}{m}}} \)
(4) \( \frac{\pi-\sin ^{-1}\left(\frac{h}{A}\right)}{2 \sqrt{\frac{k}{m}}} \)
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