A small-angle pendulum has length \(1.00\,\mathrm{m}\). Find its period using \(g=9.8\,\mathrm{m\,s^{-2}}\).

If a simple pendulum's mass is doubled, what happens to its small-angle period?

If a simple pendulum's length is increased, does its small-angle period increase or decrease?

For a pendulum with \(L=0.60\,\mathrm{m}\), find its small-angle angular frequency.

Convert a pendulum amplitude of \(6.0^\circ\) to radians for use in \(s=L\theta\).

A pendulum has period \(2.4\,\mathrm{s}\). Find its length using \(g=9.8\,\mathrm{m\,s^{-2}}\).

A pendulum length is quadrupled. By what factor does its small-angle period change?

A pendulum has length \(0.25\,\mathrm{m}\). Find its small-angle frequency in hertz using \(g=9.8\,\mathrm{m\,s^{-2}}\).

Find the length of a small-angle pendulum with period \(1.00\,\mathrm{s}\) near Earth.

A small-angle pendulum has length \(0.90\,\mathrm{m}\) and amplitude \(5.0^\circ\). Estimate its maximum arc displacement.

A pendulum is moved from a field \(g\) to a field \(g/4\), with the same length. By what factor does its small-angle period change?

A pendulum completes \(20\) small oscillations in \(36\,\mathrm{s}\). Estimate the local gravitational field strength if \(L=0.80\,\mathrm{m}\).

Starting from \(mL\ddot{\theta}=-mg\sin\theta\), show how the small-angle SHM equation is obtained and identify \(\omega\).

A small-angle pendulum has \(L=1.5\,\mathrm{m}\) and angular amplitude \(0.080\,\mathrm{rad}\). Estimate the bob's maximum speed.

A pendulum has period \(1.7\,\mathrm{s}\) when \(L=0.72\,\mathrm{m}\). Use the small-angle model to estimate \(g\).

A pendulum clock is moved to a location where \(g\) is smaller by \(4.0\%\). By approximately what percentage does its period change?

Two small-angle pendulums have the same period. One has length \(L_1\) in field \(g_1\), and the other has length \(L_2\) in field \(g_2\). Derive the relation between \(L_1,L_2,g_1,g_2\).

A pendulum is designed to have period \(T_0\) in field \(g_0\). Derive the length \(L\). Then derive the fractional period change for a small field change \(g=g_0(1+\epsilon)\), keeping first-order terms in \(\epsilon\).

A small-angle pendulum clock should keep the same period after moving from field \(g_0\) to field \(g_1\). Derive the new length in terms of the old length \(L_0\), \(g_0\), and \(g_1\), and interpret the direction of adjustment when \(g_1<g_0\).

A pendulum is mounted in an elevator accelerating upward with constant acceleration \(a_e\). Using an effective field argument, derive the small-angle period and state the model assumptions.