Question

When a mass on a spring is at maximum displacement, what quantity is at a minimum?

Answer 1

Answer:

The velocity

Explanation:

For a mass-spring system, the total mechanical energy is constant during the motion. The total mechanical energy is sum of the elastic potential energy, U, and the kinetic energy, K:

$E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2$

where

k is the spring constant

x is the displacement

m is the mass

v is the velocity

Since E must remain constant, we see that when x increases, v decreases, and vice-versa. Therefore, when x (the displacement) is at maximum, v (the velocity) is at minimum (more precisely, it is zero).