Question 12

A particle is executing simple harmonic motion. Its amplitude is $$A$$ and time period is 5 sec. The time required by it to move from $$x = A$$ to $$x = \frac{A}{\sqrt{2}}$$ is _______ sec.

$$x(t) = A \cos(\omega t)$$

$$\frac{A}{\sqrt{2}} = A \cos(\omega t)$$

$$\cos(\omega t) = \frac{1}{\sqrt{2}}$$

$$\omega t = \frac{\pi}{4}$$

$$\frac{2\pi}{T} t = \frac{\pi}{4}$$

$$t = \frac{T}{8}$$

Given $$T = 5$$: $$t = \frac{5}{8}$$

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