Question

How does the length of a pendulum string affect the frequency of oscillation?

Answer 1

Question.

How does the length of a pendulum string affect the frequency of oscillation?

Solution

The period of oscillation thread pendulum depends on its parameters as follows:

$$T = 2 \pi \sqrt {\frac {l}{g}} \quad (l - \text{the length of a pendulum, } g - \text{acceleration due to gravity}).$$

In turn, the oscillation frequency is related to the period as $f = \frac{1}{T}$.

Thus, we have $f = \frac{1}{2\pi} \sqrt{\frac{g}{l}}$.

Answer: $f = \frac{1}{2\pi} \sqrt{\frac{g}{l}}$ or $f = \frac{1}{\sqrt{l}}$.