Question

You would like a pendulum that swings back and forth once every 2 seconds, but the one you have swings once every 1.9 seconds. Which of the following should you do to adjust it so that it has the desired period?A) Remove some mass from the pendulum.
B) Make the pendulum slightly shorter.
C) Add more mass to the pendulum.
D) Make the pendulum slightly longer.

Answer 1

To decrease the period of the pendulum, B) Make the pendulum slightly shorter.  --> TRUE

Explanation:

The period of a simple pendulum is given by the equation:

$T=2\pi \sqrt{\frac{L}{g}}$

where

L is the length of the pendulum

g is the acceleration of gravity

We notice that the period of a pendulum does not depend on the mass hanging on the pendulum, but only on its length. We also notice that:

- The period is proportional to the square root of the length of the pendulum, $T\propto \sqrt{L}$

- The period is inversely proportional to the square root of the acceleration of gravity, $T \propto \frac{1}{\sqrt{g}}$

Here we want to decrease the period of the pendulum, from 2.0 s to 1.9 s. Now we can analyze the four options:

A) Remove some mass from the pendulum.  --> FALSE. The period does not depend on the mass.

B) Make the pendulum slightly shorter.  --> TRUE. Decreasing the length, L, will also decrease the period.

C) Add more mass to the pendulum.  --> FALSE. The period does not depend on the mass.

D) Make the pendulum slightly longer. --> FALSE. Increasing the length, L, will also increase the period.

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