Question: Consider a mass-and-spring system containing two masses m 1 = 1 and m 2 = 1 whose displacement functions x(t) and y(t) satisfy the differential

Consider a mass-and-spring system containing two masses m₁ = 1 and m₂ = 1 whose displacement functions x(t) and y(t) satisfy the differential equations

x"=-40x + 8y, y": = 12x - 60y.

(a) Describe the two fundamental modes of free oscillation of the system.

(b) Assume that the two masses start in motion with the initial conditions

and are acted on by the same force, F₁(t) = F₂(t) = -195 cos 7t. Describe the resulting motion as a superposition of oscillations at three different frequencies.

x"=-40x + 8y, y": = 12x - 60y.

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a The natural frequencies are 1 6 and 2 8 In mode 1 the two masses oscillate in the same di... View full answer

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