Question

The periodic time of a body executing simple harmonic motion is 3 sec. After how much interval from time t = 0, its displacement will be half of its amplitude

• A. $\frac{1}{8}$sec
• B. $\frac{1}{6}$sec
• C. $\frac{\mathbf{1}}{\mathbf{4}}$sec
• D. $\frac{1}{3}$sec

Answer 1

Answer: (C)

$\frac{\mathbf{1}}{\mathbf{4}}$sec

Answer 2

$y = a\sin\frac{2\pi}{T}t$ ⇒ $\frac{a}{2} = a\sin\frac{2\pi t}{3}$⇒ $\frac{1}{2} = \sin\frac{2\pi t}{3}$

⇒ sin$\frac{2\pi t}{3} = \sin\frac{\pi}{6}$ ⇒ $\frac{2\pi t}{3} = \frac{\pi}{6}$ ⇒ $t = \frac{1}{4}\sec$