Question

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1/a s. The value of 'a' to the nearest integer is __________.

Hint:

Time to reach $A/2$ from mean is $T/12$. Time to reach $A/2$ from extreme is $T/6$.

Answer 1

Correct Answer: 6

Step 1: Equation of SHM: $y = A \sin(\omega t)$.
Step 2: $A/2 = A \sin(\frac{2\pi}{T} t) \implies 1/2 = \sin(\frac{2\pi}{2} t) = \sin(\pi t)$.
Step 3: $\pi t = \pi/6 \implies t = 1/6 \text{ s}$.
Step 4: Given $t = 1/a \implies a = 6$.