Frequency of a pendulum executing Simple harmonic motion,

$\overline{)\begin{array}{rcl}{\mathbf{f}}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{2}\mathbf{\pi}}\sqrt{\frac{\mathbf{g}}{\mathbf{l}}}\end{array}}$

Number of oscillations,

$\overline{)\begin{array}{rcl}{\mathbf{N}}& {\mathbf{=}}& \mathbf{f}\mathbf{t}\end{array}}$

The amplitude of a damped motion,

$\overline{)\begin{array}{rcl}\mathbf{x}\mathbf{\left(}\mathbf{t}\mathbf{\right)}& {\mathbf{=}}& \mathbf{A}\mathbf{}\mathbf{e}\mathbf{x}\mathbf{p}\mathbf{}\mathbf{(}\mathbf{-}\frac{\mathbf{b}\mathbf{t}}{\mathbf{2}\mathbf{m}}\mathbf{)}\end{array}}$

**A)**

l = 13.2 m

g = 9.8 m/s^{2}

In a science museum, a 110kg brass pendulum bob swings at the end of a 13.2m -long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.7m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's damping constant is only 0.010 rm kg/s. At exactly 12:00 noon, how many oscillations will the pendulum have completed? And what is its amplitude?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Simple Harmonic Motion of Pendulums concept. You can view video lessons to learn Simple Harmonic Motion of Pendulums. Or if you need more Simple Harmonic Motion of Pendulums practice, you can also practice Simple Harmonic Motion of Pendulums practice problems.

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Based on our data, we think this problem is relevant for Professor Hergert's class at MSU.