# Answer to Question #1356 in Mechanics | Relativity for Jon ALlen

Question #1356

A visitor to a lighthouse wishes to determine

the height of the tower. She ties a spool

of thread to a small rock to make a simple

pendulum, which she hangs down the center

of a spiral staircase of the tower. The period

of oscillation is 10.8 s.

The acceleration of gravity is 9.8 m/s2 .

What is the height of the tower?

Answer in units of m.

the height of the tower. She ties a spool

of thread to a small rock to make a simple

pendulum, which she hangs down the center

of a spiral staircase of the tower. The period

of oscillation is 10.8 s.

The acceleration of gravity is 9.8 m/s2 .

What is the height of the tower?

Answer in units of m.

Expert's answer

The formula for the period of oscillations can be written as

T = 2 π √(L/g)

L = gT

L = 9.8*10.8

T = 2 π √(L/g)

L = gT

^{2}/4 π^{2}L = 9.8*10.8

^{2}/ 4π^{2}= 28.95 m.
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