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sci.simple-harmonic-oscillator Calculator
Calculates simple harmonic oscillator position, velocity, acceleration, and energy: x(t) = A cos(ωt + φ). Angular frequency ω = √(k/m) — period T = 2π/ω is independent of amplitude, which is why pendulum clocks keep accurate time for small swings.
Inputs
Mass Kg
Total mass (kg). Distinct from weight — weight = mass × gravity. Mass is constant; weight varies with location.
Spring Constant N M
Reference formula or conversion factor shown for context.
Damping Coef Ns M
Reference formula or conversion factor shown for context.
Amplitude M
Maximum displacement from equilibrium. Energy carried by a wave is proportional to amplitude squared.
Results
natural frequency ωₙ (rad/s)
Frequency at which the structure resonates freely (Hz). If machinery operates near this, resonance can amplify vibrations dangerously. Engineers detune structures to avoid it.
natural frequency fₙ (Hz)
Frequency at which the structure resonates freely (Hz). If machinery operates near this, resonance can amplify vibrations dangerously. Engineers detune structures to avoid it.
damping ratio ζ
The proportional relationship between two quantities.
damped period (s)
Reference formula or conversion factor shown for context.
initial energy (J)
Sample size or count used in the calculation.
system type
The classification or type assigned based on the inputs.