Question

Suppose you were to set up a simple pendulum experiment for which you wanted the frequency of oscillations to be 0.47 Hz. How long should you make your string in cm? (Assume this all takes place on earth.)

Answer 1

We know period of oscillation is, $T=2\pi \sqrt{\frac{L}{g}}$

Therefore, $\frac{L}{g}=\frac{1}{4\pi^2 f^2}$

Where, $T=\frac{1}{f}$

Hence, length of the string, $L=\frac{g}{4\pi^2 f^2}=\frac{980}{4\pi^2 0.47^2}\approx 52.82 cm$