Simple Harmonic Motion Calculator
Period, frequency and energy for a mass on a spring.
Work out Simple Harmonic Motion. Period, frequency and energy for a mass on a spring. Shows the working, not just the answer.
Period of oscillation
3.1416 s
0.3183 Hz · ω = 2 rad/s
The period depends on mass and stiffness only — never on amplitude. Pull the mass twice as far and it travels twice the distance at twice the speed, arriving back at exactly the same moment. That amplitude independence is what makes oscillators usable as clocks, and it is the property that fails as soon as the restoring force stops being proportional to displacement. Energy is entirely potential at the extremes and entirely kinetic at the centre, trading back and forth twice per cycle. Maximum speed happens at the equilibrium point, where the force is zero — the one place people expect the motion to be slowest.
How the Simple Harmonic Motion Calculator works
Enter mass, spring constant and amplitude for the period, frequency, maximum speed and acceleration, and the total energy. The period depends on mass and stiffness only — pull the mass twice as far and it still returns at the same moment.
Also known as: shm calculator · spring oscillation calculator · mass spring system frequency · oscillation period calculator
Frequently asked questions
How do I calculate the period of a spring oscillator?
T = 2π√(m/k). A 10 kg mass on a 40 N/m spring gives ω = 2 rad/s and a period of π seconds, about 3.14.
Does amplitude affect the period?
No, and that is the defining property of simple harmonic motion. A larger amplitude means further to travel but proportionally faster travel, so the time comes out identical. It is why oscillators work as clocks.
Where is the mass moving fastest?
At the equilibrium point, where the force is zero — the place most people expect it to be slowest. Speed is highest where displacement and force are both zero, and zero at the extremes where force is greatest.
How does energy move during the cycle?
It trades between potential and kinetic twice per cycle. Entirely potential at the extremes, entirely kinetic at the centre, with the total ½kA² constant throughout.
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