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Advanced MathQ&A LibraryTake mx′′+cx′+kx=F0cos(ωt).mx″+cx′+kx=F0cos(ωt). Fix c>0,c>0, k>0,k>0, and F0>0.F0>0. Consider the function C(ω).C(ω). For what values of mm (solve in terms of c,c, k,k, and F0F0) will there be no practical resonance (that is, for what values of mm is there no maximum of C(ω)C(ω) for ω>0ω>0)?Question

Asked Oct 31, 2019

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Take mx′′+cx′+kx=F0cos(ωt).mx″+cx′+kx=F0cos(ωt). Fix c>0,c>0, k>0,k>0, and F0>0.F0>0. Consider the function C(ω).C(ω). For what values of mm (solve in terms of c,c, k,k, and F0F0) will there be no practical resonance (that is, for what values of mm is there no maximum of C(ω)C(ω) for ω>0ω>0)?

Step 1

First find the particular solution for the differential equation-

Step 2

Auxiliary solution is

Step 3

Substitute the obtained solution...

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