JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Elasticity & SHM

A simple harmonic oscillator has an amplitude A and time period

6 π

second. Assuming the oscillation starts from its mean position, the time required by it to travel from

x = A

x = \frac{3}{2} A

will be

\frac{π}{x} s

, where

x =

______:

Answer: 2

Solution

With the oscillation starting from the mean position,

x (t) = A sin (ω t)

. On the reference circle, as the particle moves from

x = A

x = \frac{3}{2} A

, the corresponding phase angle

ϕ

satisfies

cos ϕ = \frac{3 /2 A}{A} = \frac{3}{2} ⟹ ϕ = \frac{π}{6}

With

ω = \frac{2 π}{T} = \frac{2 π}{6 π} = \frac{1}{3}

, the time elapsed is

t = \frac{ϕ}{ω} = \frac{π /6}{1/3} = \frac{π}{2}

Comparing with the given form

t = \frac{π}{x}

gives

x = 2

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Integer answer