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Question 10

The motion of a simple pendulum executing S.H.M. is represented by the following equation $$y = A \sin(\pi t + \phi)$$, where time is measured in second. The length of pendulum is

The motion of a simple pendulum executing SHM is: $$y = A\sin(\pi t + \phi)$$, where time is in seconds.

Comparing with $$y = A\sin(\omega t + \phi)$$:

$$\omega = \pi \text{ rad/s}$$

$$T = \frac{2\pi}{\omega} = \frac{2\pi}{\pi} = 2 \text{ s}$$

For a simple pendulum: $$T = 2\pi\sqrt{\frac{L}{g}}$$

$$2 = 2\pi\sqrt{\frac{L}{g}}$$

$$1 = \pi\sqrt{\frac{L}{g}}$$

$$\frac{L}{g} = \frac{1}{\pi^2}$$

$$L = \frac{g}{\pi^2} = \frac{9.8}{9.8696} \approx 0.9929 \text{ m} = 99.29 \text{ cm}$$

This is approximately 99.4 cm.

Hence, the correct answer is Option C: 99.4 cm.

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