Chapter 11, Problem 7Q

What happens to the period of a playground swing if you rise up from sitting to a standing position?

To determine

The effect on the period of a playground swing if one rises from sitting to a standing position.

Answer to Problem 7Q

Solution:

The period of the swing will decrease and the frequency will increase.

Explanation of Solution

When one rises to a standing position, the center of mass rises (or it moves towards the pivot point) and effectively shortens the length of the swing. The period of the swing will decrease.

From the simple pendulum $T=2\pi \sqrt{\frac{L}{g}}$

  $f=\frac{1}{T}=\frac{1}{2\pi }\sqrt{\frac{g}{L}}$

Conclusion: The period of the swing will decrease as the length of the pendulum effectively decreases.