Question:

The frequency of oscillation is higher if the spring is stiffer and the mass is larger. Why?

Answer:

Firstly, let’s remind ourselves of the defining equation for simple harmonic motions

From this equation, we realize that the ω (and thus f) of a simple harmonic motion is decided by the acceleration to displacement ratio of the system. Basically, the frequency depends on how fast the restoring force can accelerate the displaced system back towards the equilibrium position.

The stiffer the spring, the larger restoring force per unit change in extension. This, coupled with a smaller mass, results in a larger acceleration per unit displacement. With a few lines of algebra, you should be able to derive the frequency for a spring-mass system to be

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