When an oscillatory system is displaced from its equilibrium position, and then released, it goes into oscillation. Basically, if an oscillating mass is subjected to only the restoring force (i.e. no damping force and no external driving force), the resulting oscillation is called a free oscillation.

It turns out that for a SHM, *a*=-*ω*^{2}*x*. This means that the *a*/*x* ratio determines the frequency of oscillation.

With this in mind, we can understand why for a spring-mass system, a stiffer spring (increases the restoring force per unit displacement) and a smaller mass (increases the acceleration for the same restoring force) results in a higher frequency of oscillation. In fact, it can be derived quite easily that for a spring-mass system *ω*^{2}=*k*/*m*.

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A pendulum is another famous SHM. The derivation is more complicated but it can be shown that for a pendulum *ω*^{2}=*g*/*L*. (Notice the amplitude has no effect on the period of oscillation?)