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*Question:* Having landed on a newly discovered planet, an astronaut sets up
a simple pendulum of length , and finds that it makes 51 complete
oscillations in 1 minute. The amplitude of the oscillations is small compared to the
length of the pendulum. What is the surface gravitational acceleration on the planet?
*Answer:* The frequency of the oscillations is

Hence, the angular frequency is

Now,
for small amplitude oscillations of a simple pendulum. Rearrangement off this formula gives

Hence, the surface gravitational acceleration is
.

Richard Fitzpatrick
2006-02-02