In order for mechanical oscillation to occur, a system must posses two quantities: elasticity and inertia. When the system is displaced from its equilibrium position, the elasticity provides a restoring force such that the system tries to return to equilibrium. The inertia property causes the system to overshoot equilibrium. This constant play between the elastic and inertia properties is what allows oscillatory motion to occur.
The animated gif shows the simple harmonic motion of three undamped mass-spring systems, with natural frequencies (from left to right) of ωo, 2ωo, and 3ωo. All three systems are initially at rest, but displaced a distance xm from equilibrium.
Source:http://www.acs.psu.edu/drussell/Demos/SHO/mass.html
Reference:http://farside.ph.utexas.edu/teaching/315/Waves/node4.html
http://scipp.ucsc.edu/~haber/ph5B/sho09.pdf
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