What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where the restoring force is proportional to the displacement.

Simple harmonic motion (SHM) is a type of periodic motion where the restoring force is proportional to the displacement. This means that the force acting on the object is directly proportional to the distance it is displaced from its equilibrium position. The most common example of SHM is the motion of a mass attached to a spring, where the force exerted by the spring is proportional to the displacement of the mass from its equilibrium position.

The equation of motion for SHM is given by x = A cos(ωt + φ), where x is the displacement of the object from its equilibrium position, A is the amplitude of the motion, ω is the angular frequency, t is the time, and φ is the phase angle. The angular frequency is related to the period of the motion by T = 2π/ω, where T is the period.

The velocity and acceleration of the object in SHM can also be expressed in terms of the displacement. The velocity is given by v = -Aω sin(ωt + φ), and the acceleration is given by a = -Aω^2 cos(ωt + φ). These equations show that the velocity and acceleration are also periodic functions of time, with the same frequency as the displacement.

SHM has many applications in physics and engineering, including in the design of oscillating systems such as pendulums, springs, and electrical circuits. Understanding the properties of SHM is essential for many areas of physics and engineering, and is a fundamental concept in A-Level Maths.