Chapter 14, Problem 92GP

In Section 14–5, the oscillation of a simple pendulum (Fig. 14–46) is viewed as linear motion along the are length x and analyzed via F = ma. Alternatively, the pendulum’s movement can be regarded as rotational motion about its point of support and analyzed using τ = Iα. Carry out this alternative analysis and show that

$\theta (t)={\theta }_{\max }\cos \left(\sqrt{\frac{g}{\mathcal{l}}}t+\varphi \right),$

where θ(t) is the angular displacement of the pendulum from the vertical at time t, as long as its maximum value is less than about 15°.

FIGURE 14–46

Problem 92.