Graphing

Simple Harmonic Motion Calculator

Calculate simple harmonic motion (SHM) displacement with amplitude, frequency, phase shift, and time. Visualize SHM graphs and copy results easily.

Parameters

Enter the parameters for Simple Harmonic Motion calculation.

The displacement x(t) is calculated using the formula: x(t) = A * cos(2π * f * t + φ)

units
Hz
radians

Enter comma-separated values for time.

Displacement Values

SHM Visualization

Understanding Simple Harmonic Motion

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. It's often visualized as the projection of uniform circular motion onto a diameter. Examples include a pendulum swinging with a small angle, a mass-spring system, and oscillations in electrical circuits.

  • Amplitude (A): The maximum displacement from the equilibrium position.
  • Frequency (f): The number of oscillations per unit time, measured in Hertz (Hz).
  • Phase Shift (φ): Determines the initial position of the oscillation at time t=0.
  • Formula: The displacement x(t) at time t is given by: x(t) = A * cos(2π * f * t + φ)

Learn more about SHM on Wikipedia.

Frequently Asked Questions

What is the Simple Harmonic Motion Calculator?
The Simple Harmonic Motion Calculator is an online Graphing calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Simple Harmonic Motion Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Simple Harmonic Motion Calculator for professional Graphing projects?
Yes. The math behind it is standard Graphing, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Simple Harmonic Motion Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Simple Harmonic Motion Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.

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