Answer to Question #160909 in Classical Mechanics for Ulrich

Question

A simple pendulum has a period of 2.5 s. What is its period if its length is made four times larger?

Answer 1

The period of the pendulum can be written as follows:

$$T=2\pi \sqrt{\dfrac{L}{g}}.$$

If the length of the pendulum is four times larger, then the period will be:

$$T_{new}=2\pi \sqrt{\dfrac{4L}{g}}=2\cdot2\pi \sqrt{\dfrac{L}{g}}=2T,$$ $$T_{new}=2\cdot2.5\ s=5\ s.$$