Coupled Oscillator: Jonathan Schreven

Coupled Oscillator System

In this problem I would like to explore the solution of a double spring/mass system under the assumption that the blocks are resting on a smooth surface. Our system might look something like this.

Using F=ma we can then find our equations of equilibrium.

\begin{aligned} F & = m a \\ F & = m \ddot{x} \\ - k_{1} x_{1} - k_{2} (x_{1} x_{2}) & = m_{1} \ddot{x_{1}} \\ - \frac{k_{1} x_{1}}{m_{1}} - \frac{k_{2} (x_{1} - x_{2})}{m_{1}} & = m_{1} \ddot{x_{1}} \\ - \frac{k_{1} x_{1}}{m_{1}} - \frac{k_{2} (x_{1} - x_{2})}{m_{1}} & = \ddot{x_{1}} \\ - \frac{k_{1} + k_{2}}{m_{1}} x_{1} + \frac{k_{2}}{m_{1}} x_{2} & = \ddot{x_{1}} \end{aligned}

Coupled Oscillator: Jonathan Schreven

Coupled Oscillator System

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