Introduction. Simple harmonic motion shown both in real space and phase space
Simple harmonic motion shown both in real space and phase space. The orbit is periodic. (Here the velocity and position axes have been reversed from the standard convention in order to align the two diagrams)
A simple harmonic oscillator of the spring, and the other end of the spring is connected to a rigid support such as a wall. If the system is left at rest at the equilibrium position then there is no net force acting on the mass. However, if the mass is displaced from the equilibrium position,a restoring elastic force which obeys Hooke's law is exerted by the spring.
Mathematically, the restoring force F is given by
where F is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and x is the displacement from the equilibrium position (in m).
Every simple harmonic oscillator exhibits a characteristic feature.
- When the system is displaced from equilibrium position, a restoring force which obeys Hooke's law exists and tend to restore the system to its equilibrium.
Once the mass is displaced from its equilibrium position, it experiences a net restoring force. Hence, it accelerates and starts going back to the equilibrium position. When the mass moves closer to the equilibrium position, the restoring force decreases. At the equilibrium position, the net restoring force vanishes. However, at x = 0, the momentum of the mass does not vanish due to the impulse of the restoring force that has acted on it. Therefore, the mass shoots past the equilibrium position compressing the spring. A net restoring force then tends to slow it down, until its velocity vanishes, whereby it will attempt to reach equilibrium position again.
As long as the system has no energy loss, the mass will continue to oscillate. Thus, the simple harmonic motion is known as one of the periodic motions.