Question

A man builds a grandfather clock and wants the pendulum to complete one oscillation every 4.00 seconds.What is the period of the clock’s pendulum?What is the frequency of the clock’s pendulum?How long does the pendulum need to be?

Answer 1

Given:

The pendulum completes one oscillation every 4 seconds.

To find the time period, frequency, and length of the pendulum.

Step-by-step explanation:

The time period is the time taken to complete one oscillation, so the time period is

`T\text{ = 4 s}`

The frequency will be

`\begin{gathered} f=(1)/(T) \\ =(1)/(4) \\ =0.25\text{ Hz} \end{gathered}`

The length of the pendulum is

`\begin{gathered} T=2\pi\sqrt{(l)/(g)} \\ l=(T^2)/(4\pi^2)g \end{gathered}`

Here, g =9.8 m/s^2 is the acceleration due to gravity.

On substituting the values, the length will be

`\begin{gathered} l=((4)^2*9.8)/(4*(3.14)^2) \\ =3.97\text{ m} \end{gathered}`

Thus, the length of the pendulum is 3,97 m.

Final answer:

The time period is 4 s.

The frequency is 0.25 Hz.

The length of the pendulum is l = 3.97 m.