Question
Asked Oct 5, 2019
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Solve the given initial-value problem. (Assume 
ω ≠ γ.)
d2x
dt2
+ ω2x = F0 cos(γt),  x(0) = 0,  x'(0) = 0
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Expert Answer

Step 1

Find the homogeneous solution of the given IVP as follows.

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The given IVP is as follows, d'x x Fcos(yt), x(0)= x'(0)= 0 and m Y + x=Fcos (7t), x(0)=x'(0) = 0 and y x Consider the homogeneous part x" + o'x= 0 The characteristice equation is m2 +@ = 0. m2 =0 m2 = -02 m-i, i The homogeneous solution is x C cos (t)+C, sin(0t)

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Step 2

Find the particular solution of ...

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The IVP isx" + o'x= F cos(yt), x(0) = x'(0)= 0 and oy Let the particular solution be of the form, x Acos(yt) =-yAsin(y --ycos(yt) х -ycos(yt)+wAcos(yt)= F cos(yt) Ao2-72F JA=+ O#0 is x, +Ycos(yt). The particular solution is x,

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