Oscillations: Simple Harmonic Motion

Simple Harmonic Motion

Simple harmonic motion (SHM) refers to a type of periodic motion where the restoring force is directly proportional to displacement but acts in the opposite direction.
The object in SHM moves back and forth through a fixed point known as the equilibrium position.
SHM can be represented by the equation a = -ω²x, where a is acceleration, ω is angular frequency, and x is displacement.
Displacement, velocity, and acceleration are key aspects of SHM. Displacement is the distance moved from equilibrium, velocity is speed in a given direction and acceleration results from changes in velocity.
Examples of SHM include a swinging simple pendulum and the oscillations of a mass-spring system.

Simple Harmonic Motion: Displacement, Velocity and Acceleration

Displacement (x) is measured from the equilibrium position. It is maximal at the extremes of the motion and zero at the equilibrium.
Velocity (v) of an object in SHM is maximum at the equilibrium position and zero at the extremes of the motion. It acts in the opposite direction to displacement.
Acceleration (a) is always directed towards the equilibrium position and is maximum at the extremes of the motion. It’s directly proportional to displacement but in the reverse direction.

Simple Harmonic Motion: Energy

Energy in SHM is constant. It gets transferred between potential and kinetic energy.
When the object is at the extremes, potential energy is at maximum and kinetic energy is zero. As the object moves towards equilibrium, potential energy decreases while kinetic energy increases.
At the equilibrium position, kinetic energy is maximum and potential energy is zero.
These energy changes can be represented graphically, with kinetic and potential energy as sinusoidal curves that are 90 degrees out of phase.

Remember, understanding the principles behind these concepts is key. Practice applying these in solving problems and make sure to incorporate past question practice.