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Two identical masses are are copuled to 3 springs in a linear fashion as shown. The system is arranged such that each spring is unstretched when the...

Two identical masses are are copuled to 3 springs in

a linear fashion as shown. The system is arranged such that

each spring is unstretched when the system as at rest. This

system has two normal modes of oscillation

a.) Describe the motion of the masses for the lowest and

excited normal modes

b.) Find the frequency of oscillation for each normal mode

c.) Imagine mass mA is displaced some amount, xo, while

mass mB is held fixed, and the system is then released.

Starting from the general result derrived in class for two coupled oscillators with identical mass,

namely

xA = Ccos(wot + phase0) + Dcos(w1t + phase1)

xB = Ccos(wot + phase0) - Dcos(w1t + phase1)

Show that each mass undergoes a periodic oscillation with a time varying amplitude (i.e. "beating").

d) What is the period of the beating?

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