Question

The pendulum of an antique clock has been damaged and needs to be replaced. If the original pendulum completed one swing every 1.5 seconds, how long should the new pendulum be? Use the formula:
T=2π√ L/980

Answer 1

\[T = 2 \pi \sqrt {\frac{ l }{ g }}\]
where T is the period (time taken for one full swing), l is length of string, and g is the gravitational acceleration of 9.8m/s^2

The original period is 1.5s
Thus we need to find l, so solve:
\[T = 1.5s = 2 \pi \sqrt{\frac{ l }{ g }} \]
\[\sqrt{\frac{ l }{ g }} = \frac{ 1.5 }{ 2 \pi } \rightarrow \frac{ l }{ g } = (\frac{ 1.5 }{ 2\pi })^2 \rightarrow l = g(\frac{ 1.5 }{ 2\pi })^2\]