Mechanical Simple Harmonic Oscillators (SHO)

References

Simple Harmonic Motion

The Physics Classroom

Dan Russell's (Kettering University)  Acoustics and Vibration Animations

Phasors and Sinusoids

Examples of Mechanical Simple Harmonic Oscillators


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Simple Pendulum







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Spectrum of a Tuning Fork


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An important calculation - the resonant frequency of a simple harmonic oscillator:

Consider a specific kind of resonator or harmonic oscillator - e.g., a pendulum or a tuning fork - and suppose that



Newton tells us that for any mechanical system



However, harmonic oscillators follow Hooke's law so that



Putting these two relationship together we have



Symbolically
where


We now "guess" the solution
           

(click on image to enlarge)

Phasor Representation


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so that


Thus, this solution works if