Does an increase in the restoring force of a spring increase its frequency?

[manohman]

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If the restoring force is larger, then the system, whether pendulum or spring, should return to equilibrium faster (higher acceleration) right?

So restoring force and frequency should be proportional?

 

[NextStepTutor_3]

Well, the angular frequency of a spring is equal to the square root of k/m, and restoring force = -kx. So a higher value for k would lead both to greater restoring force and greater frequency. But note that the only two values that can affect frequency are k and m! In other words, frequency is independent of x. So be careful - for example, if you double restoring force by doubling x, you still don't change frequency.