A spring with spring constant k = 13-N/m and length L = 26.0-cm has masses m = 1

Question

A spring with spring constant k = 13-N/m and length L = 26.0-cm has masses m = 12-g attached at each end of the spring, and is placed on a frictionless table. Both masses are pulled x = 4.3-cm from equilibrium and released.

What is the period of oscillation of the individual masses?   What is the maximum potential energy stored in the spring?

2)A simple pendulum oscillates with period TE = 24.9-s on Earth. I take the pendulum to Planet X, and find the oscillation period there to be TX = 37.5-s. Suppose Planet X has the same mass as Earth. What is its radius? (The radius of Earth is 6371-km.)

Explanation / Answer

2)

For a pendulum
T = 2pisqrt(L/g)
T^2 = 4pi^2L/g
TE^2/TX^2 = 4pi^2L/gE/4pi^2L/gX

TE^2/TX^2 = gX/gE

Newtons law of gravitation
F = Gm1m2/r^2
Newtons second law
F = ma
and so
F/m =a = Gm2/r^2
so for the same mass,
gE and gX are inversly proprotional to radius
TE^2/TX^2 = gX/gE = rE^2/rX^2
TE/TX = rE/rX
24.9/37.5 = 6371/rX
rX = 6371*37.5/24.9 = 9595 km

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