Simple harmonic motion is a type of periodic motion in which the restoring force on an object is directly proportional to the object's displacement from its equilibrium position. This results in a sinusoidal motion, where the object oscillates back and forth around its equilibrium point.
The period of a simple harmonic motion can be calculated using the formula T = 2π√(m/k), where T is the period in seconds, m is the mass of the object in kilograms, and k is the spring constant in newtons per meter.
Damping is a force that opposes the motion of an object, causing its velocity to decrease over time. In simple harmonic motion, damping decreases the amplitude of the oscillations and changes the period of the motion. A higher damping coefficient results in quicker decay of the oscillations.
An underdamped system experiences oscillations with a decreasing amplitude. A critically damped system returns to its equilibrium position without any oscillations. An overdamped system returns to its equilibrium position slowly and without any oscillations.
Simple harmonic motion can be observed in many natural phenomena, such as the motion of a pendulum, the vibration of a guitar string, and the motion of a mass on a spring. It also has practical applications in engineering and technology, such as in the design of shock absorbers and oscillating systems for timekeeping devices.