Question

In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum’s damping constant is only 0.010 kg/s. At exactly 12:00 noon, how many oscillations will the pendulum have completed and what is its amplitude?

Short answer

Part A

Part B

Step-by-step solution

Part A

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

Number of Oscillations = n

$$\begin{gathered} n=t\frac{\varpi }{2\pi }=4\times 3600\times \sqrt{\frac{9.8}{15}-\frac{0.{01}^2}{4\times {110}^2}}/2\pi \\ n=1852.5 \end{gathered}$$

Part 2

Amplitude = 0.780 m

$$\begin{gathered} A\left(t\right)=A{e}^{\frac{-t}{2\tau }}=1.5\times e^{(-t/2\times 11000)}=1.5\times e^{(-4\times 60\times 60÷22000)} \\ A\left(t\right)=0.780m \end{gathered}$$