An object of mass 1 (kg) stretches a spring and is set in motion from a certain position. The damping constant of the spring is 2 (N · 8/m), and the spring constant in Hooke's law is 5 (N/m). During the motion there is an external force f(t) (N) acting on the mass such that f(t) = Acos(w(t – 4)). Then the displacement y = y(t) of the object from the equilibrium position satisfies /" + 2y' + 5y = A cos(w(t – $)).
An object of mass 1 (kg) stretches a spring and is set in motion from a certain position. The damping constant of the spring is 2 (N · 8/m), and the spring constant in Hooke's law is 5 (N/m). During the motion there is an external force f(t) (N) acting on the mass such that f(t) = Acos(w(t – 4)). Then the displacement y = y(t) of the object from the equilibrium position satisfies /" + 2y' + 5y = A cos(w(t – $)).
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Transcribed Image Text:Question 9
An object of mass 1 (kg) stretches a spring and is set in motion from a certain position. The
damping constant of the spring is 2 (N s/m), and the spring constant in Hooke's law is
5 (N/m). During the motion there is an external force f(t) (N) acting on the mass such that
f(t) = Acos(w(t – ø)). Then the displacement y = y(t) of the object from the equilibrium
position satisfies
y" + 2y' + 5y = Acos(w(t – ¢)).
(a) Find the general solution of y when A = 1, w = 1 and ó = 0.
(b) Find the general solution of y when A = 1, w = 2 and ø = 5.
(c) If the damping constant is 0, then for what values of A, w and o does resonance occur
in the system? Justify your answers.
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