Question

During one complete oscillation of a mass on a spring (oneperiod), what is the change in potential energy of the mass+spring system, in the absence of friction?

Short answer

During one complete oscillation of a mass on a spring the change in potential energy of the mass and spring system collectively in the absence of friction is 0 J.

Step-by-step solution

Understanding the potential energy

The energy owned by a body as a result of its position, shape, or change of configuration is called as potential energy.

Calculation of potential energy of the mass and the string system

It can be assumed that no non-conservative work is done on the spring-mass system since there is no friction.

Write the equation for work done on the spring.

$E_f=E_i+W_{NC}$

Here$E_f$ is the final energy,$E_i$ is the initial energy and$W_{NC}$ is the work done by non-conservative force.

It is known from basic harmonic motion theory that the spring-mass system returns to its starting position after one oscillation (if energy is conserved). As a result, it is deduced that not only mechanical energy, but also potential energy, is conserved that is,

$∆U=0\mathrm{J}$

Thus, the change in potential energy of the mass and spring system, in the absence of friction is 0 J.