Question

In a spring-mass oscillator, when is the magnitude of momentum of the mass largest: when the magnitude of the net force acting on the mass is largest, or when the magnitude of the net force acting on the mass is smallest?

Short answer

The magnitude of the momentum of mass is largest when the magnitude of the net force acting on the mass is largest.

Step-by-step solution

Spring-mass system

A spring-mass system is a spring system with a block hanging or connected at the free end. Any item executing a basic harmonic motion may generally be found using the spring-mass system.

Explanation

Expression for the spring-mass system

$mx+kx=F_s$

Where is the mass of an object, $x$ is the displacement of an object, $k$ is the stiffness of spring, and $F_s$ is the force applied to the object.

As the above equation shows, as the momentum of mass is largest, then the net force acting on the mass is largest.

Thus, in a spring-mass oscillator, the magnitude of the momentum of mass is largest when the magnitude of the net force acting on the mass is largest.