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: A.0.25 centimetersB.234.8 centimetersC.55.9 centimetersD.351 centimeters

Answer 1

Answer: We essentially have to find the variable L, provided the value of the duration of one complete swing, or the period:

`T=2\pi\sqrt{(L)/(980)}\Rightarrow(1)`

The value of the variable T is a known quantity in the equation (1), therefore plugging it into the equation (1) gives the following equation:

`(1.5)=2\pi\sqrt{(L)/(980)}\Rightarrow(2)`

The solution is found by solving for the variable L in the equation (2), the steps for the answer are as follows:

`\begin{gathered} \begin{equation*} (1.5)=2\pi\sqrt{(L)/(980)} \end{equation*} \\ \\ \\ ((3)/(2))=2\pi\sqrt{(L)/(980)} \\ \\ (1)/(2\pi)*(3)/(2)=\sqrt{(L)/(980)} \\ \\ \\ ((1)/(2\pi)*(3)/(2))^2=(L)/(980)\rightarrow((1)/(4\pi^2)*(9)/(4))=(L)/(980)\Rightarrow(1)/(\pi^2)*(9)/(16)=(L)/(980) \\ \\ \\ L=((980*9)/(16))*(1)/(\pi^2)=(2205)/(4)*(1)/(\pi^2) \\ \\ \\ L=55.853302482 \\ \\ \\ L\approx55.9cm \end{gathered}`

The answer is 55.9 centimeters or Option C.