Question

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.)?

Answer 1

Using the period formula T = 2π√(L/g) for a simple pendulum and rearranging it to solve for the length L, we find that a pendulum must be approximately 15.92 meters long to have a period of one swing every 8 seconds, with a gravity acceleration of 9.80 m/s².

Step-by-step explanation:

To find out how long a simple pendulum must be for it to have a period of one swing per four seconds, we need to use the formula for the period T of a simple pendulum, which is T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. In this case, since one complete oscillation takes 8.0 seconds, and the period is the time for one cycle, we have T = 8.0 s. The acceleration due to gravity g is typically 9.80 m/s².

Rearranging the formula to solve for L, we get L = (T/2π)² * g. Substituting T = 8.0 s and g = 9.80 m/s² into the formula, we can calculate the necessary length of the pendulum. After performing the calculation, we find that the length L required for a pendulum to have a period of 8 seconds is approximately 15.92 meters.

Answer 2

The period T is the time it takes the pendulum to make one complete oscillation. T = 8.0s. But T= 1/f. Where again T is the time and f is the frequency. So f = 1/8 = 0.125s.