Simple Harmonic Motion Simple harmonic motion is a type of motion in which an object moves back and forth along a straight line, with the motion being period...
Simple harmonic motion is a type of motion in which an object moves back and forth along a straight line, with the motion being periodic and the displacement from its equilibrium position being simple harmonic.
Imagine a mass attached to a spring, and the spring is stretched to its full length. When the mass is released, it starts to oscillate back and forth along the line. The motion of the mass is simple harmonic because its position can be described by a single parameter, such as its position along the line.
The motion of a simple harmonic oscillator can be described by a single equation:
where:
x(t) is the position of the object at time t
A is the amplitude of the motion, which is half the distance between the maximum and minimum positions
(\omega) is the angular frequency of the motion, which is the rate at which the position of the object repeats itself
t is the time
The angular frequency (\omega) is related to the period (T) of the motion through the equation:
The period (T) is the time taken for the object to complete one oscillation, and it is equal to the time taken for the spring to complete one stretch and release cycle.
Simple harmonic motion occurs when the restoring force is proportional to the displacement from the equilibrium position. This means that the force acting on the object is equal to a negative times the displacement from the equilibrium position. The force is positive when the object is moving towards the equilibrium position, and negative when the object is moving away from the equilibrium position.
Examples of simple harmonic motion include the motion of a pendulum, a mass attached to a spring, and a vibrating string