Chapter 14, Problem 58P

(II) A physical pendulum consists of an 85-cm-long. 240-g-mass, uniform wooden rod hung from a nail near one end (Fig 14–38). The motion is damped because of friction in the pivot; the damping force is approximately proportional to dθ/dt. The rod is set in oscillation by displacing it 15° from its equilibrium position and releasing it. After 8.0s, the amplitude of the oscillation has been reduced to 5.5°. If the angular displacement can be written as θ = Ae^-γt cos ω′t, find (a) γ, (b) the approximate period of the motion, and (c) how long it takes for the amplitude to be reduced to $\frac{1}{2}$ of its original value.

FIGURE 14–38

Problem 58.