| A simple pendulum is constructed by attaching a mass m to a thin rod of length \[\ell \]. The pendulum is pulled back to some angle \[\theta >30{}^\circ \] from the vertical and released. Which of the following techniques could be used to change the frequency f of this pendulum? |
| I. Changing the mass m on the end of the pendulum |
| II. Changing the length \[\ell \] for the pendulum |
| III. Changing the angle \[\theta \] from which the pendulum is released |
A) I only
B) I and II only
C) II only
D) II and III only
Correct Answer: D
Solution :
[D] For small angles of \[\theta \] (typically less than\[15{}^\circ ),\]the frequency of oscillation for a simple pendulum is approximately. \[f=\frac{1}{T}=\frac{1}{2\pi }\sqrt{\frac{g}{\ell }}\] For increasingly large value of however, the acceleration no longer varies linearly with displacement. Thus, for larger angles, the frequency f will be a affected by the angle of release \[\theta ,\]as well as by the length of the pendulum.
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