Simple Harmonic Motion Calculator
Calculate displacement, velocity, and acceleration in simple harmonic motion using trigonometry
About this calculator
The Simple Harmonic Motion Calculator helps students, engineers, and physicists analyze oscillatory systems by computing displacement, velocity, and acceleration at any point in time. This tool uses fundamental trigonometric principles to solve complex harmonic motion problems instantly, eliminating manual calculations and reducing errors. Whether studying pendulums, springs, or wave mechanics, this calculator provides accurate results for understanding periodic motion behavior in various physical systems.
How to use
Enter the amplitude, angular frequency, initial phase, and time value into the calculator. The tool will automatically compute the displacement using sine/cosine functions, velocity by taking the first derivative, and acceleration through the second derivative. Results are displayed instantly with proper units for immediate analysis.
Frequently asked questions
What is simple harmonic motion?
Simple harmonic motion is periodic oscillation where restoring force is proportional to displacement, like a mass on a spring or pendulum swinging.
How do I find angular frequency?
Angular frequency (ω) equals 2π divided by period (T), or can be calculated from spring constant and mass (ω = √(k/m)).
Why use trigonometric functions for SHM?
Trigonometric functions naturally describe periodic motion, with sine and cosine representing smooth oscillations between maximum positive and negative values.