When the acceleration of a mass on a spring is zero, the velocity is at a
.

When the velocity of a mass on a spring is zero, the acceleration is at a
.

1) Maximum

2) Maximum

Explanation:

The force acting on a mass on a spring is given by Hooke's law; in magnitude:

where

F is the force

k is the spring constant

x is the displacement

Also we know from Newton's second law that we can write

where

m is the mass

a is the acceleration

So we can write the equation as

(1)

From this relationship, we see that the acceleration is directly proportional to the displacement.

On the other hand, we know that the total mechanical energy of the system mass-spring is constant, and it is given by

(2)

where the first term is the elastic potential energy while the second term is the kinetic energy, and where

v is the velocity of the mass

From eq. (2), it is clear that when displacement increases, velocity decreases, and vice-versa; however, from eq.(1) we also know that acceleration is proportional to the displacement.

Therefore this means that:

- When acceleration increases, velocity decreases

- When acceleration decreases, velocity increases

Therefore, the two answers here are:

- When the acceleration of a mass on a spring is zero, the velocity is at a  maximum

When the velocity of a mass on a spring is zero, the acceleration is at a  maximum

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