Question

A particle of mass 0.1kg is in SHM of amplitude 0.1m.When the particle passes through its mean position its kinetic energy is 8x10-3J. At what position will its kinetic energy reduce to half this value? What will be the potential energy at this position?

Answer 1

Dear Student,

Sum of potential energy and kinetic energy is constant in a SHM.

Also, at extreme kinetic energy is zero and at mean position potential energy is zero

$$\begin{gathered} Given, \\ A=0.1m, \\ \frac{1}{2}k{A}^2=8\times {10}^{-3}[Askineticenergyiszero,potentialenergyisequaltototalenergy] \\ k{(0.1)}^2=16\times {10}^{-3} \\ k=1.6 \\ Whenkineticenergyishalfpotentialenergyisalsohalf \\ \frac{1}{2}k{x}^2=\frac{8\times {10}^{-3}}{2} \\ 1.6x^2=8\times {10}^{-3} \\ {x}^2=\frac{8\times {10}^{-3}}{1.6}=5\times {10}^{-3} \\ x=\sqrt{5\times {10}^{-3}}m \end{gathered}$$


Regards