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Simple Harmonic Motion Calculator

Physics
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Analyzes oscillatory motion (like a mass on a spring) calculating frequency, period, displacement, velocity, and acceleration.

How To Use

How to use this calculator

Start with your values, or try a preset.

Step 1

Enter Amplitude (A), Angular Frequency (ω), Time (t), and Phase Constant (φ) in the units shown.

Step 2

Read Acceleration (a), Velocity (v), Displacement (x), Frequency (f), and Period (T) in the results panel. Results update as you change the inputs.

Step 3

Choose a preset to load an example, then adjust the values for your situation.

Worked Examples

Example calculations

See the inputs and their calculated results.

Example 1

Amplitude (A): 0.1 m; Angular Frequency (ω): 2 rad/s; Time (t): 0.5 s; Phase Constant (φ): 0 rad

Acceleration (a): -0.2161209223 m/s²; Velocity (v): -0.168294197 m/s; Displacement (x): 0.05403023059 m; Frequency (f): 0.318310155 Hz; Period (T): 3.14159 s

Example 2

Amplitude (A): 0.2 m; Angular Frequency (ω): 3 rad/s; Time (t): 1 s; Phase Constant (φ): 0.5 rad

Acceleration (a): 1.685622037 m/s²; Velocity (v): 0.2104699366 m/s; Displacement (x): -0.1872913375 m; Frequency (f): 0.4774652326 Hz; Period (T): 2.094393333 s

Example 3

Amplitude (A): 0.15 m; Angular Frequency (ω): 4 rad/s; Time (t): 0.25 s; Phase Constant (φ): 0.2 rad

Acceleration (a): -0.8696586107 m/s²; Velocity (v): -0.5592234516 m/s; Displacement (x): 0.05435366317 m; Frequency (f): 0.6366203101 Hz; Period (T): 1.570795 s

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