For a particle performing S.H.M., when displacement is 'x', the potential energy and restoring force acting…

For a particle performing S.H.M., when displacement is 'x', the potential energy and restoring force acting on it is denoted by 'E' and 'F' respectively. The relation between $\mathrm{x}, \mathrm{E}$ and $\mathrm{F}$ is
  1. $\frac{E}{F}+x=0$
  2. $\frac{2 E}{F}+x=0$
  3. $\frac{E}{F}-x=0$
  4. $\frac{2 E}{F}-x=0$

Solution

Displacement $=x, \quad$ P.E. $=E, \quad$ Force $=F$ $F=-k x$ $E=\frac{1}{2} m \omega^{2} x^{2}=\frac{1}{2} k x^{2}$ $2 E=(-) \frac{F}{x} \times x^{2}=(-) F x$ $\frac{2 E}{F}+x=0$

Asked in: MHT CET 2020 (16 Oct Shift 1)

Practice more Oscillations questions on Aicharya