Example 10  Keeping Time

Determine the length of a simple pendulum that will swing back and forth in simple harmonic motion with a period of 1.00 s.

Reasoning  When a simple pendulum is swinging back and forth in simple harmonic motion, its frequency f is given by Equation 10.16 as , where g is the acceleration due to gravity and L is the length of the pendulum. We also know from Equation 10.5 that the frequency is the reciprocal of the period T, so . Thus, the equation above becomes . We can solve this equation for the length L of the pendulum.

Solution The length of the pendulum is

Figure 10.23 shows a clock that uses a pendulum to keep time.
This pendulum clock keeps time as the pendulum swings back and forth. ( Robert Mathena/ Fundamental Photographs)
Figure 10.23  This pendulum clock keeps time as the pendulum swings back and forth. (© Robert Mathena/ Fundamental Photographs)



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