Question

Make the solution clear please.

Differential Equations course, topic: RLC circuits Exercises Exercise 1. By directly substituting the series expressions (3) and (4) into (2), and then comparing the Fourier coefficients of both sides, express co, cn and dn in terms of ao, an and bnYou may assume y(t) is sufficiently smooth for its Fourier series to be twice-differentiated term-wise LCy"(t)RCy(t)+ y(t) = x(t) nat nnt bn sin (t) =lo an Cos n-1 nnt nat +da sin y(t)= = Co+ Cn COS n-1 IM8 IM8

Answer 1

lasSmate Dete Poge aiven t SLO ITth Siniitt dn n cosinTt (snT 4-P p cansidex LC ylet tRC yt) +4t) 2 -LC cont dh < )nf RC t dnnrco3 t Cn cos No LC)d n(RC) (os Co+ ラ en 2 dn (-Lc)+Gh (-RC)t dn Ocb (4n (es hT + bh Sinnirt Compaivisg 2. fRC)+E -7 く =4。 dn Sa

Dche Pora maltiply tey (e PR assins w 4ex (RC RC dn t hiT nil multiply by Adainy get n Thenefore Cp and Ca=9o asan coekirient