Answer to Question #236184 in Classical Mechanics for alwande hadebe

Question

The figure shows two equal masses connected by a spring with two other identical springs fixed to rigid supports on either side. This system permits the masses to jointly undergo simple harmonic motion along a straight line such that the system corresponds to two couple oscillators. (a) Explain clearly why the equations of motion of the two masses should be mx¨1 + k(2x1 − x2) = 0, mx¨2 + k(2x2 − x1) = 0 for mass m1 and mass m2 respectively. (b) Show that the system possesses two characteristic frequencies, one out of phase (fast) and the other in phase (slow), ωf = r 3k m and ωs = r k m . Note that there are numerous different ways of finding these frequencies from the equations of motion. These include assuming oscillatory motion of each mass, algebraically manipulating the equations of motion or solving the eigenvalue problem

Answer 1

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