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How long must a simple pendulum be if it is to make exactly one swing per...

How long must a simple pendulum be if it is to make exactly one swing per four seconds? (That is, one complete oscillation takes exactly 8.0 s.)

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Answer #1
Concepts and reason

The concepts used to solve this problem are the oscillatory motion and the time period of oscillation.

Use the expression for period of oscillation of simple pendulum to obtain the expression for the length of simple pendulum.

Then, use the time taken, and acceleration due to gravity to find the value for the length of simple pendulum.

Fundamentals

The expression for period of oscillation of simple pendulum is given below:

-
DO

Here, the period of oscillation is , the length of the pendulum is , and the acceleration due to gravity is .

The expression for period of oscillation of simple pendulum is given below:

-
DO

Rearrange the above expression by squaring both sides.

5.
7

The expression for the length of the simple pendulum is as follows:

 =1

Substitute for , for and 9.81 m/s
for .

T=20,le
(8 s)’x9.81 m/s2
4x3.142
627.84 m
39.43
= 15.91 m

Hence, the required length of simple pendulum must be 15.91 m
long.

Ans:

The simple required length of the pendulum must be 15.91 m
long.

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