You want to use a pendulum clock on the moon $$g $=1\mathrm{.}625$ m $.$ m s$2$

a$)$What length should the pendulum have in order for it to have a period of T $=1\mathrm{.}00$s$?[6$pt$.]$

b$)$Now you need a clock for your trip into interstellar space. A pendulum clock won$$t work, even while

moving with a constant velocity. Why? $[3$pt$.]$

c$)$You then decide to create a clock from a spring and an object with a mass m $=655$g$.$ What is the amplitude of the spring if it has a maximum velocity of vmax $=0\mathrm{.}5$ms $,$ and a period of T $=1\mathrm{.}00$s$?[8$pt$.]$