Question

2. Solve for the motion of a driven-damped harmonic oscillator whose forcing function F(t) is given by F(t) = 0, < 0 HU t 12 0 <t<T PO) – 4(), 0<t<7 F(t) = A, t>t. m т.

Answer 1

According to the General Question. The motion of a ginen duinen damped harmonic or callatos whore facing function f(t) es ginen ky EG) - 0 ; txo - ()*: oct 27 f(1) 4; t.se As we know that equation of a motion Calea + op og net ws] 96 = f(d) -->0 By using Grecis fuction det Gilde,tthe the Green Facken 9. Geltu). Š(+-+) --☺ the g()' = FLtGild,t") d' Dy (D = 0 F (8) GC4,4)*

eqn o becomes SºfW) D a Cd,t) dx = 5 FLt)5(4+) ' EF (0 En - Applying fourier traspora B edes () du Gill, t'); het -w2ta poftwa By entegrating we get to 6(4,1) - a len tt) ott) ewhere to wot-pt aza Bird B² wa barpo JB² wa (t-t) ... so, tet, : l", tst': St* Te L. - e. . Hari . so G (t, t') a e weep(tt) 128*(1+) 234+1) 812-t) Solation to ean ④ R yld - Gas Silo). colt e) { $42-) 21146)ste=)

i olt-t') pas non zoo during tot y lo Fu] 2:8 4+) {cile 4). {1*4 +) sacos elét) set (04-+5)*7 d Elt) p*4 + sin(( t-tnať As our question of gewn as F(t) =0,20 f(0 = Am (& ockq F(t) = domi tyt cry (S Aiman (1)* * (l+" sim (364-4.5)dt tiistam e-817-t5([ 2-+5)d"