A 100$100$ gram mass is at rest on a frictionless air track glider. The length of the track is 2$2$ meters and the mass is initially set at the midpoint. The mass is attached to a spring, k =50$=50$ Newtons/$/$meter,$,$ which is anchored to one end of the track. The mass is pulled back 0.75$0\mathrm{.}75$ meters and allowed to oscillate along the track.

a. Find the amount of work down in extending the spring 0.75$0\mathrm{.}75$ meters

b. What force was applied to the spring in order to extend it 0.75$0\mathrm{.}75$ meters?

c. After releasing the mass, find its maximum velocity.

d. At what point does the oscillating mass reach maximum velocity?

e.  Draw a graph of potential energy and kinetic energy as the glider oscillates from +$+$X to −$-$ X.$.$  Include units.