Determine the variables on which a pendulum's amplitude (or sometimes called the pendulum position) depends (see Fig. 11.2).  Use the Buckingham \(\pi\) theorem; the relevant dimensional variables can be listed as pendulum's mass \((m)\), length of the rigid rod \((l)\), pendulum's period \((\tau)\), time \((t)\), gravitational acceleration \((g)\), and initial position of the pendulum \(\left(\phi_{0}=\phi(0)ight)\).

FIGURE 11.2 m