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?

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

where A=maximum Amplitude

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

where x=compression in the spring

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

i.e.

Total energy

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

the closer the planet is to the sun, the larger the gravity

answer: 31, 5556. 952 seconds