JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Elasticity & SHM

A particle executes S.H.M. with amplitude '

a

' and time period '

T

'. The displacement of the particle when its speed is half of maximum speed is

\frac{x a}{2}

. The value of

x

is ____

Answer: 3

Solution

In SHM the speed at a displacement

y

from the mean position is

v = ω a^{2} - y^{2}

, and the maximum speed is

ω a

. Setting

v = \frac{ω a}{2}

ω a^{2} - y^{2} = \frac{ω a}{2} \Rightarrow a^{2} - y^{2} = \frac{a ^{2}}{4}

y^{2} = \frac{3 a ^{2}}{4}

and

y = \frac{3 a}{2}

. Matching this against

\frac{x a}{2}

gives

x = 3

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Numerical answer