JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Elasticity & SHM

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is

\frac{3 E}{4}

then its displacement '

y

' is given by:

Answer: (A)

Solution

In simple harmonic motion the total energy is

E = \frac{1}{2} m ω^{2} a^{2}

and the kinetic energy at displacement

y

\frac{1}{2} m ω^{2} (a^{2} - y^{2})

. Setting the kinetic energy equal to

\frac{3 E}{4}

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

The displacement at that instant is

y = \frac{a}{2}

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Single correct option