A block of mass m is moving with an initial velocity `v_0` towards a stationary spring of stiffness k attached to the wall as shown in figure

a. Find the maximum compression in the spring.
b. Is the work done by the spring negative or positive?

Explanation

The force exerted by the spring is opposite to the displacement of the block. Therefore, the work done by the spring force is negative.
Let `x_0` be the maximum compression in the spring, then work done by spring force on the block
`W=-underset0overset(x_0)intkxdx=-1/2kx_0^2`
If we consider a block in the system. The external force acting on the block is spring force. Using work-energy theorem,
`W=DeltaK=K_f-K_i`
`implies-1/2kx_0^2=0-1/2mv_0^2impliesx_0=v_0sqrt(m/k)`