A particle performs S.H.M. from the mean position. Its amplitude is 'A' and total energy is 'E'. At a…

A particle performs S.H.M. from the mean position. Its amplitude is 'A' and total energy is 'E'. At a perticular instant its kinetic energy is $\frac{3 \mathrm{E}}{4}$. The displacement of the particle at that instant is
  1. $A$
  2. $\frac{A}{8}$
  3. $\frac{A}{4}$
  4. $\frac{A}{2}$

Solution

Total energy $=\mathrm{E}=\frac{1}{2} \mathrm{~m} \omega^{2} \mathrm{~A}^{2}$ When kinetic energy is $\frac{3 \mathrm{E}}{4}$, its potential energy is $\left(\mathrm{E}-\frac{3 \mathrm{E}}{4}\right)=\frac{\mathrm{E}}{4}$ Dividing Eq.(1) by Eq.(2), $\quad 4=\frac{A^{2}}{x^{2}} \quad \therefore x=\frac{A}{2}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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