A mass-spring system driven by a sinusoidal external force is governed by the following nonhomogeneous differential equation: y′′(t) + by′(t) + 2y(t) = 4cos(2t) (a)Find the values of the constant b for which the homogeneous system is underdamped, overdamped, and critically damped. (b) For b = 1, (i) find the equation of motion yh(t) of the free system; (ii) determine a particular solution yp(t) to the forced system; (iii) write down a general solution y(t) to the forced system
A mass-spring system driven by a sinusoidal external force is governed by the following nonhomogeneous differential equation: y′′(t) + by′(t) + 2y(t) = 4cos(2t) (a)Find the values of the constant b for which the homogeneous system is underdamped, overdamped, and critically damped. (b) For b = 1, (i) find the equation of motion yh(t) of the free system; (ii) determine a particular solution yp(t) to the forced system; (iii) write down a general solution y(t) to the forced system
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A mass-spring system driven by a sinusoidal external force is governed by the following nonhomogeneous differential equation:
y′′(t) + by′(t) + 2y(t) = 4cos(2t)
(a)Find the values of the constant b for which the homogeneous system is underdamped, overdamped, and critically damped.
(b) For b = 1,
(i) find the equation of motion yh(t) of the free system;
(ii) determine a particular solution yp(t) to the forced system;
(iii) write down a general solution y(t) to the forced system
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