Given:
The pendulum completes one oscillation every 4 seconds.
To find the time period, frequency, and length of the pendulum.
Explanation:
The time period is the time taken to complete one oscillation, so the time period is
[tex]T\text{ = 4 s}[/tex]The frequency will be
[tex]\begin{gathered} f=\frac{1}{T} \\ =\frac{1}{4} \\ =0.25\text{ Hz} \end{gathered}[/tex]The length of the pendulum is
[tex]\begin{gathered} T=2\pi\sqrt{\frac{l}{g}} \\ l=\frac{T^2}{4\pi^2}g \end{gathered}[/tex]Here, g =9.8 m/s^2 is the acceleration due to gravity.
On substituting the values, the length will be
[tex]\begin{gathered} l=\frac{(4)^2\times9.8}{4\times(3.14)^2} \\ =3.97\text{ m} \end{gathered}[/tex]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.