Question

1. determine the natural frequency of a pendulum whose length is 15 ft.

Explanation:

Step1: Recall the formula for the natural frequency of a pendulum

The formula for the natural frequency \( f \) of a pendulum is \( f=\frac{1}{2\pi}\sqrt{\frac{g}{L}} \), where \( g = 32.2\space ft/s^{2} \) (acceleration due to gravity) and \( L \) is the length of the pendulum.

Step2: Substitute the given values into the formula

Given \( L = 15\space ft \) and \( g=32.2\space ft/s^{2} \).

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Step3: Calculate the value of \( f \)

$$ f=\frac{1.465}{2\pi}\approx\frac{1.465}{6.283}\approx0.233\space Hz $$

Answer:

The natural frequency of the pendulum is approximately \( 0.233\space Hz \)