Calculate the position, velocity, and acceleration of an object undergoing simple harmonic motion at any given time.
Last updated: March 2026 | By ForgeCalc Engineering
Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction. Common examples include a mass on a spring, a simple pendulum, and the vibration of atoms in a crystal.
In SHM, the object oscillates around a central equilibrium position. The motion is characterized by its amplitude (maximum displacement), frequency (number of oscillations per second), and phase (the starting position of the oscillation).
Angular frequency (ω = 2πf) represents the rate of change of the phase of the oscillation in radians per second. It is a key parameter in the trigonometric functions describing SHM.
In SHM, acceleration is always proportional to displacement but in the opposite direction (a = -ω²x). This is because the restoring force always pulls the object back toward the equilibrium position.
The phase constant (or phase shift) determines the starting position of the object at t=0. If φ=0, the object starts at its maximum positive displacement (A).
A real pendulum only undergoes SHM for 'small angles' (typically less than 15°). At larger angles, the restoring force is no longer strictly proportional to the displacement, and the motion becomes more complex.
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