Question

Why is the restoring force in Hooke's law a negative value?

Answer 1

It's a negative value because the negative sign on the spring's force means the force exerted opposes the spring's displacement

Answer 2

Explanation:

Hooke's law :

According to the Hooke's law, The force is the directly proportional to the displacement of the string.

On the other hand,

In a simple harmonic motion, The restoring force is directly proportional to the displacement and acts in the opposite direction to that of displacement.

The restoring force is defined as,

$F\propto -x$

$F = -kx$

Where,

F = restoring force

k = restoring constant

x = displacement

The negative sign shows the force opposes the string's displacement