Question

Can a spring constant be negative?

Answer 1

Restoring Force:

1. The restoring force $F=-kx$, acts opposite to the applied force.
2. The spring constant $k$, is always positive to support the fact that it will oppose the applied external force.
3. If the spring constant is to be negative it will imply that if you compressed a spring even slightly it would then compress itself further, which is not possible physically.

No, the spring constant cannot be negative.