A spring with stiffness ks and relaxed length L stands vertically on a table. You hold a mass M just barely touching the top of the spring. (a) You very slowly let the mass down onto the spring a...

A spring with stiffness ks and relaxed length L stands vertically on a table. You hold a mass M just barely touching the top of

the spring.

(a) You very slowly let the mass down onto the spring a certain distance, and when you let go, the mass doesn't move.

How much did the spring compress? How much work did you do?

(b) Now you again hold the mass just barely touching the top of the spring, and then let go. What is the maximum

compression of the spring? State what approximations and simplifying assumptions you made.

(c) Next you push the mass down on the spring so that the spring is compressed an amount s, then let go, and the mass

starts moving upward and goes quite high. When the mass is a height of 2L above the table, what is its speed?