In a science museum, a 140 kg brass pendulum bob swings at the end of a 11.1 m -

Question

In a science museum, a 140 kg brass pendulum bob swings at the end of a 11.1 m -long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.6 m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's damping constant is only 0.010kg/s.

part A)

At exactly 12:00 noon, how many oscillations will the pendulum have completed?

Express your answer as an integer.

Part B

What is its amplitude at noon?

Express your answer to two significant figures and include the appropriate units

Explanation / Answer

A) The damping time constant is = m/b = 14000s.n = t*(w/2pi)

                     = 4*3600*sqrt[(9.8/11.1) – (0.01^2/(4*140^2))/2pi] = 2153.45

B) A(t) = A*exp(-t/2*tau) = 1.6*exp(-t/(2*14000))

Therefore, t = 4*60*60 sec

A(t) =1 .6*exp(-(4*3600)/(2*14000)) = 0.957 m

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