## Answers

o 2116 + 8 dy mdy at2 tky = to cos (nt) dt 9) Y p (t) = A cosnt + B sinnt Yp' (t) = - An sinnt + Bn cosnt Yp" (t) = -An² cosnt - B h² sinnt L-Anscount - Bn sinnt) +8 [Ansinnt + Bh Cosnt +K[A cosnt +B sinnt +] = Fo Cosnt On comparing coefficient of sinnt Bram m - An8 +KB = 0 B (k-1 min) Comparing coefficient of cont - Amn + Bn8 + AK= Fo A [K-mn?] + Bn8=Fo B {(k-me?) + (nr3²] = Fo no

B = Fo hr (K-mn ²)2 + n²g2 A = Fo (K-mn²) (k-mn 2)2 + 2282 Cosnt + Fong sinht Yp (t) = Fo (k-m2²) (k-mn]2+ n²82 (k-mn ²)2 +2282 b) (k-min²) cosnt Yp (t) = Fo Fo V(k-mn ² +2782 + nr sinnt v (km2) 2222 Vik-mn 2)2 +2222 cos o 2 ut K-mn² (k-mn 2 2 2 2 2 2 than = sind hr v (kmn2 + 272 Yp (t) J (k-mn 2+2 222 cosnt cosp + sinnt sind [ con lnt-d)] Fo Yp (t) v (k-mn 27 1282 where c = Fo J (K-mn ²)²+ nr ² et

for (max with no respect to c this should be so X = (k-mn ² 2 + n² myn = 0 dX dn 2 (K-mn ²) (2mn) +2n8² n(82 - 2 m (k-mn²)) =0 82 - 2m (k-mn² = 0 2 m (k-mn²) Y? K-mn? 82 2 m mn² = k-82 2 m Y? 2 m2 m n=J&K 2 2 m2 Cmax Fo v (x - (K-21 ) )2 + ( + 1 - 2 2 2 (max - 84 4m² + kr²_84 m 2 m2

Cmax = 2 fom учKm — 82 re 12km then Charactestic eqn mo 2 + 87 tk=0 Ta -8 + 582_4km 2 m = – ri i 54 km - 82 2 m sinut loswt te e at Ya(t) = ci è at with a= 8 w = 34 km-82 2 m 2 m 80 (n.) + 1 k у rm2 +22 4m2 2 2 + 18 r 4m2 =w2 m 2m Since w= 4km-82 2 m Ell rece

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