JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Elasticity & SHM

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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

\frac{1}{a} s

. The value of 'a' to the nearest integer is ______

Answer: 6

Solution

Measured from the mean position,

x = A sin ω t

with

ω = \frac{2 π}{T} = \frac{2 π}{2} = π

rad/s. Setting

x = \frac{A}{2}

sin π t = \frac{1}{2} \Rightarrow π t = \frac{π}{6} \Rightarrow t = \frac{1}{6} s

Hence

a = 6

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Integer answer

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