A spring-loaded toy gun is used to shoot a ball of mass M straight up in the air. The ball is not attached to the spring. The ball is pushed down onto the spring so that the spring is compressed a distance S below its unscratched point. After release, the ball reaches a maximum height 35, measured from the unscratched position of the spring (see diagram). a) Find the spring constant of the spring. Height Spring b) Find the equilibrium point of the ball when it is sitting on the spring with no forces other than gravity and the spring acting on it. Clearly indicate the point you are using as the origin of your coordinate system and what direction is positive. | 1fa = 11 c) Now, the ball is glued onto the spring so that it oscillates up and down rather than flying off the spring. The spring is again compressed the same distance 5 below its unscratched point. Write an equation for the position of the ball as a function of time after it is released. Clearly indicate the point you are using as the origin of your coordinate system and what direction is positive.​