Why is the restoring force in Hooke's law a negative value?
It's a negative value because the negative sign on the spring's force means the force exerted opposes the spring's displacement
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