The best example for a simple harmonic oscillator is a loaded horizontal spring. With in the elastic limits the spring follows Hook’s law and has a force constant ‘k’ when the spring is stretched by a small amount, the restoring force F is directly proportional to the extension or compression in a direction opposite to it. By placing a mass ‘m’ on an air track, it can slide on a smooth frictionless surface. Stable position of the block is when it is neither be compressed nor elongated.
Let this position be x=0. Now if we displace it by doing some work on it and leave it, the block tries to seek back its real position due to elasticity of the spring, which provides the necessary restoring force. When the mass reaches the equilibrium position, it keeps on going and stops at some point in opposite direction. Once again it proceeds for its return trip. This to and fro motion is called oscillation. This system oscillates with a fixed frequency whatever amplitude it is. This happens with in the elastic limits only. The frequency is called the natural frequency.
The force law for this motion is given by,
F = -kx
Where F is the restoring force, k is the spring constant
According to Newton
F = ma
ma = -kx
a = (-k*x)/m
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