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A mass-spring-dashpot system is described by my?? + cy? + ky = Fo cos ?t, see §3.6...

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Advance Math

A mass-spring-dashpot system is described by

my?? + cy? + ky = Fo cos ?t,


see §3.6 Eq. (17). This second-order differential equation has beenused in simulations, such as this

one at the PhET site:https://phet.colorado.edu/en/simulation/legacy/resonance.

For m = 2.53kg, c = 0.502N/(m/s), k = 97.2N/m, Fo =97.2×0.5N = 48.6N,and ? = 2.6, the equation becomes


2.53y?? + 0.502y? + 97.2y = 48.6 cos(?t) .......................(1)

(a) Given the initial value

y(0) = 2.20, y?(0) = 0,


solve Eq. (1), Round to three significant figures. Show all yourwork, and clearly highlight your

conclusion—the combination of complementary function andparticular solution.

(b) From your particular solution, which is of the form

yp =Acos?t+Bsin?t,

calculate the amplitude, which is ?(A2 + B2). Clearly highlightyour conclusion—the amplitude. You are encouraged to use the PhETsimulation to verify your amplitude. Note that the angularfrequency ? = 2?f where f is the frequency in the simulation.

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