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 below. (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 x(0)=21, x'(0)=4, and y(0) = 33, y'(0) = 2 and are acted on by the same force F₁ (t)= F₂(t)= 1080 cos (7t). Describe the resulting motion as a superposition of oscillations at three different frequencies. X'= -7x+6y y' =9x-22y (a) The lower frequency mode has ₁ : amplitude of the oscillation of m₂ is The masses oscillate in times the amplitude of the oscillation of m₁. and the

Elements Of Electromagnetics
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Consider a mass-and-spring system containing two masses m, = 1 and m2 = 1 whose displacement
functions x(t) and y(t) satisfy the differential equations below. (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 x(0) = 21, x'(0)= 4, and y(0) = 33, y'(0) = 2 and are acted on by the same force
F, (t) = F2(t) = - 1080 cos (7t). Describe the resulting motion as a superposition of oscillations at three
different frequencies.
x'" = - 7x + 6y
y" = 9x - 22y
...
(a) The lower frequency mode has w, =
The masses oscillate in
and the
amplitude of the oscillation of m2 is O times the amplitude of the oscillation of m,.
Transcribed Image Text:Consider a mass-and-spring system containing two masses m, = 1 and m2 = 1 whose displacement functions x(t) and y(t) satisfy the differential equations below. (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 x(0) = 21, x'(0)= 4, and y(0) = 33, y'(0) = 2 and are acted on by the same force F, (t) = F2(t) = - 1080 cos (7t). Describe the resulting motion as a superposition of oscillations at three different frequencies. x'" = - 7x + 6y y" = 9x - 22y ... (a) The lower frequency mode has w, = The masses oscillate in and the amplitude of the oscillation of m2 is O times the amplitude of the oscillation of m,.
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