Simple Harmonic Motion vs Periodic Motion
Periodic motions and simple harmonic motions are two very important types of motions in the study of physics. A simple harmonic motion is a good model to understand the complex periodic motions. This article will explain what periodic motion and simple harmonic motion are, their applications, similarities and finally their differences.
A periodic motion can be considered as any motion that repeats itself in a fixed time period. A planet revolving around the sun is a periodic motion. A satellite orbiting around the earth is a periodic motion even the motion of a balance ball set is a periodic motion. Most of the periodic motions we encounter are circular or semi-circular. A periodic motion has a frequency. The frequency means how “frequent” the event occurs. For simplicity, we take frequency as the occurrences per second. Periodic motions can either be uniform or nonuniform. A uniform periodic motion can have a uniform angular velocity. Functions such as amplitude modulation can have double periods. They are periodic functions encapsulated in other periodic functions. The inverse of the frequency of the periodic motion gives the time for a period. Simple harmonic motions and damped harmonic motions are also periodic motions.
Simple Harmonic Motion
The simple harmonic motion is defined as a motion taking the form of a = – (ω2) x, where “a” is the acceleration and “x” is the displacement from the equilibrium point. The term ω is a constant. A simple harmonic motion requires a restoring force. The restoring force can be a spring, gravitational force, magnetic force or an electric force. A simple harmonic oscillation will not emit any energy. The total mechanical energy of the system is conserved. If the conservation does not apply, the system will be a damped harmonic system. There are many important applications of simple harmonic oscillations. A pendulum clock is one of the best simple harmonic systems available. It can be shown that the period of the oscillation does not depend on the mass of the pendulum. If external factors such as air resistance affect the motion, it will be eventually dampened and will stop. A real-life situation is always a damped oscillation. The spring mass system is also a good example for the simple harmonic oscillation. The force created by the elasticity of the spring acts as the restoring force in this scenario. The simple harmonic motion can also be taken as the projection of a circular motion with a constant angular velocity. At the equilibrium point, the kinetic energy of the system becomes a maximum, and at the turning point, the potential energy becomes maximum and kinetic energy becomes zero.
What is the difference between Periodic Motion and Simple Harmonic Motion?
• Simple harmonic motion is a special case of periodic motion.
• Simple harmonic motion requires a restoring force, but there can be periodic motions, without restoring forces.
• A simple harmonic motion conserves its total mechanical energy, but a periodic system doesn’t necessarily have to do so.