Coupled Oscillator: Jonathan Schreven: Difference between revisions
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Using F=ma we can then find our equations of equilibrium. | Using F=ma we can then find our equations of equilibrium. | ||
:<math>F=ma | |||
:<math>\begin{alignat}{3} | |||
F & = ma \\ | |||
F & = m\ddot{x} \\ | |||
-k_{1}x_{1}-k_{2}(x_1x_2) & = m_1\ddot{x_1} \\ | |||
-{k_1x_1 \over {m_1}}-{k_2(x_1-x_2) \over {m_1}} & = m_1\ddot{x_1} \\ | |||
-{k_1x_1 \over {m_1}}-{k_2(x_1-x_2) \over {m_1}} & = \ddot{x_1} \\ | |||
-{k_1+k_2 \over {m_1}}x_1+{k_2 \over {m_1}}x_2 & = \ddot{x_1} \\ | |||
\end{alignat}</math> | |||
Revision as of 18:27, 9 December 2009
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.