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

Step-by-step 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=(1)/(2)kA^2`

where A=maximum Amplitude

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

`U=(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`

`(1)/(2)kA^2=2U`

`(1)/(2)kA^2=(1)/(2)kx^2`

`A^2=2x^2`

`x=(A)/(√(2))`

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