Question

Ratio of kinetic energy at mean position to potential energy at A/2 of a particle performing SHM​

Answer 1

▶ Solution :

Given :

A particle is performing SHM

To Find :

Ratio of kinetic energy at mean position to potential energy at A/2

Formula :

▪ Formula of kinetic energy of a particle in SHM is given by

$\boxed{\bf{\pink{KE=\dfrac{1}{2}k(A^2-X^2)}}}$

▪ Formula of potential energy of a particle in SHM is given by

$\boxed{\bf{\red{PE=\dfrac{1}{2}kX^2}}}$

• X denotes distance from mean position
• A denotes amplitude
• k = mω$^2$

Calculation :

$\mapsto\sf\:\dfrac{KE}{PE}=\dfrac{(A^2-X^2)}{X^2}\\ \\ \mapsto\sf\:\dfrac{KE}{PE}=\dfrac{A^2-0^2}{(\frac{A}{2})^2}\\ \\ \mapsto\boxed{\bf{\orange{KE:PE=4:1}}}$