A block (mass m ) hangs from a spring (spring constant k ). The block is release

Question

A block (mass m) hangs from a spring (spring constant k). The block is released from rest a distance d above its equilibrium position.

(a) What is the speed of the block as it passes through the equilibrium point? (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)
v =  

(b) What is the maximum distance below the equilibrium point that the block will reach? (Use any variable or symbol stated above along with the following as necessary:g for the acceleration due to gravity.)
x =

Explanation / Answer

As spring force is a conservative force, so total energy remains conserved,

As inititally it is compressed so, 1/2kd2 + mgd = 1/2 mv2

Find out velocity.

b) Max distance is when velocity becomes zero,

From the equilibrium point let the distance be h

So, mgh = 1/2kh2

h= 2mg/k

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