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# Simple Harmonic Motion:Oscillation of 2 blocks with 3 spring

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The word document has a graph that is necessary to understand the problem, please go directly there.

A harmonic force [F0 sin wt)] is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 be the deviations from equilibrium for m1 and m2, respectively. Ignore gravity.

1) Write the equations of motion. Use x1 and x2 as your variables.
2) Find the normal frequencies of the system, that is, when the external force is absent. Assume for this part and the remainder of the problem the springs are the same and the masses are equal.
3) Solve for the steady state motion, that is find x1 and x2 as functions of time. (Hint: Assume complex solutions.)

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#### Solution Preview

Please see the attached file.

Here's the problem written in crystal clarity.

A harmonic force [F0 sin(ωt)] is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 ¬be the deviations from equilibrium for m1 and m2, respectively. Ignore gravity.

1) Write the equations of motion. Use x1 and x2 as your variables.
2) Find the normal frequencies of the system, that is, when the external force is absent. Assume for this part and the remainder of the problem the springs are the same and the masses are equal.
3) Solve for the steady state motion, that is find x1 and x2 as functions of time. (Hint: Assume complex solutions.)

Just to clarify, in this graph, the masses and springs are all riding on a frictionless plane. Nothing is vertical and gravity is thus not involved.

this will help me ...

#### Solution Summary

A complex combination of springs and blocks with a periodic force.

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