What is the equation of motion for simple harmonic motion?

The equation of motion for simple harmonic motion is x = A cos(ωt + φ).

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. The equation of motion for simple harmonic motion is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude of the motion, ω is the angular frequency, t is time, and φ is the phase angle.

The angular frequency ω is related to the period T of the motion by the equation ω = 2π/T. The period T is the time taken for one complete oscillation. The frequency f of the motion is the reciprocal of the period, f = 1/T.

The velocity and acceleration of an object undergoing simple harmonic motion can also be described by equations. The velocity v is given by v = -Aω sin(ωt + φ), and the acceleration a is given by a = -Aω^2 cos(ωt + φ). These equations show that the velocity is maximum when the displacement is zero, and the acceleration is maximum when the displacement is at its maximum.

The equation of motion for simple harmonic motion is used to describe a wide range of phenomena, from the motion of a mass on a spring to the vibrations of atoms in a crystal lattice. Understanding the equation of motion is essential for understanding the behaviour of these systems.