# Oscillator Chain Resonance

The Oscillator Chain Resonance model displays the total mechanical energy as a function of frequency in a chain of coupled oscillators. The chain is driven at one end by a sinusoidal force Fdrive =sin(ωt) and the total energy is measured after skipping a large number of drive cycles to allow the system to reach steady state. Particles are also subject to a small damping force FStokes= - bv to remove transients and to limit the amplitude of the oscillation.

For a simple one-dimensional Hooke's Law model with spring constant k, the kinetic energy of the i-th particle is Ki= (1/2)Mvi2 and potential energy of each spring is Ui= (1/2) kΔyi2. The total energy E = U + K for a lattice of N molecules is the sum of these energies.

Note that the first particle (i=0) is not used when computing energy because its motion is not governed by Newton's second law.

## References:

- Vibration and Wave Physics 3 ed by Iain G. Main, Cambridge (1993). See Chapter 9 for a discussion of power and input impedance.

### Note:

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