Question

Consider a ball of mass m attached to a spring of stiffness k, oscillating with amplitude A on a frictionless horizontal surface. At what displacement from equilibrium does the system have equal quantities of kinetic and potential energy?

Answer 1

Answer:

Explanation:

Given

mass of ball is m

Spring constant is k

If a ball is undergoing a SHM motion then the total energy associated with it is

Total Energy $T=\frac{1}{2}kA^2$

where A=maximum Amplitude

Elastic Potential Energy of the system at any moment is given by

$U=\frac{1}{2}kx^2$

where x=compression in the spring

moment at which kinetic(K) and potential energy(U) are equal

i.e. $K=U$

Total energy$=K+U$

$\frac{1}{2}kA^2=2U$

$\frac{1}{2}kA^2=\frac{1}{2}kx^2$

$A^2=2x^2$

$x=\frac{A}{\sqrt{2}}$

i.e. at x=0.707 A kinetic energy and potential energy are equal