What is the motion equation for simple harmonic motion?

The motion equation 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 motion equation for simple harmonic motion is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency (2π times the frequency), t is time, and φ is the phase angle (initial displacement at t=0).

The equation can also be written in terms of sine instead of cosine: x = A sin(ωt + φ). The choice of sine or cosine depends on the initial conditions of the motion.

The velocity and acceleration equations for simple harmonic motion can be derived by taking the first and second derivatives of the motion equation, respectively. The velocity equation is v = -Aω sin(ωt + φ), and the acceleration equation is a = -Aω^2 cos(ωt + φ).

The period of simple harmonic motion is the time it takes for one complete cycle of motion. It can be calculated using the equation T = 2π/ω, where T is the period and ω is the angular frequency.

In summary, the motion equation for simple harmonic motion is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. The velocity and acceleration equations can be derived by taking the first and second derivatives of the motion equation, respectively. The period of simple harmonic motion can be calculated using the equation T = 2π/ω.