Three masses and four springs are connected as shown above between two fixed wal

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Three masses and four springs are connected as shown above between two fixed walls. As shown, each spring is at its equilibrium position. Define omega^2=k/m and let x1 measure the displacement of mass m to the right from equilibrium. Similarly x2 and x3 measure the displacement to the right of 2m and 4m respectively. 1. Write the coupled differential equations describing the motion of this system. 2. Assume a complex exponential time behavior for the coordinates x1, x2, and x3 with amplitudes of A, B, and C respectively (for example x1 = A e i alpha t ). Write the coupled algebraic equations for the motion of this system. 3. Write the single equation which must be solved to determine values of alpha which yield non-trivial solutions for the motion of this system.

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