Simple Harmonic Motion Calculator
Calculate position, velocity, and acceleration in SHM.
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Enter the amplitude, angular frequency, time, and optional phase offset. The calculator shows the position, velocity, acceleration, and period of the oscillation at the specified time.
About Simple Harmonic Motion
Simple harmonic motion is the most fundamental type of oscillation in physics. It occurs in systems where the restoring force is proportional to displacement, such as mass-spring systems and small-angle pendulums. The motion is described by x(t) = A cos(omega t + phi), where A is amplitude, omega is angular frequency, and phi is phase. Velocity and acceleration are obtained by differentiation. SHM is central to understanding waves, vibrations, and AC circuits.
Frequently Asked Questions
What is simple harmonic motion?
Simple harmonic motion (SHM) is oscillation where the restoring force is proportional to displacement. The motion is sinusoidal: x(t) = A cos(omega t + phi).
What is the relationship between SHM and circular motion?
SHM is the projection of uniform circular motion onto a diameter. The angular frequency of SHM equals the angular velocity of the corresponding circular motion.
What determines the period of SHM?
The period T = 2 pi / omega depends only on the angular frequency, which is determined by the system properties (spring constant and mass, or pendulum length and gravity). Amplitude does not affect the period.