Question

A block of mass m is attached to a spring with spring constant k and free to slide along a horizontal frictionless surface. At t=0, the block spring system is stretched on amount x>0 from the equilibrium position and is released from rest Vx = 0
What is the period of oscillation of the block?
What is the velocity of the block when it first comes back to the equilibrium position?

Answer 1

The period of oscillation of the block is
T=2π√(m/k)
From the conservation of energy:
(kx^2)/2=(mv^2)/2.
The velocity of the block when it first comes back to the equilibrium position:
v=x√(k/m).