An astronaut wants to determine the mass of objects she finds inspace. On Earth she chooses a spring and attaches a rock to it thatweighs 20 N. After placing the rock on a horizontal table, andattaching the spring horizontally to a fixed point, she stretchesthe rock 2 cm from equilibrium, in the positive direction. She thenreleases it from rest. After 30 s has passed, she finds that therock has gone through 10 cycles and is at a new positive maximumvalue, which is 1 cm from equilibrium. (a) What is the period ofthe oscillation? (b) What is the spring constant of the spring? (c)What is the time constant of the decay? (d) Find a function thatdescribes the motion, including damping, of the spring and masssystem that is only a function of time. Assume time starts when themass is released. (e) Roughly sketch (1) the position vs time and(2) velocity vs time of this setup. (f) Later, during the returnfrom a mission on Mars (no gravity), she wants to know the mass ofan unknown rock she’s found. This rock is attached to the samespring, which is now attached to the wall of the spacecraft. Themass is disturbed from equilibrium and the period of the resultingoscillations is found to be 2 s. What is the ratio of the mass ofthe new rock to the mass of the rock found on Earth?