Below we have given the solution to the resistence free vibrating system with periodic forcing f(t), unit mass and unit spring constsnt: y'' + y = f(t), y(0)=0 and y'(0)=0. The solution is given by y(t) = 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 Below we have given several different 2\317\200-periodic f(t). We have plotted f(t) and the solution. Check them out and decide whether or not you think resonance has occurred. Also, look at section 7.6 in the text, especially equations (11) and (13) on pg 417 of new text and pg 391 of old text. The function g(t) below plays the same role as the function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJURidGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGKy9GOVEnbm9ybWFsRic= in the text. Try out some other 2\317\200 periodic functions and see what you get. f := t -> abs(sin(t)); plot(f(t),t=0..20); y := t -> int(sin(t-s)*f(s),s=0..t); plot(y(t),t=0..40); f := t -> abs(sin(t)-1/2); plot(f(t),t=0..20); y := t -> int(sin(t-s)*f(s),s=0..t); plot(y(t),t=0..40); f := t -> abs(sin(t))-1/2; plot(f(t),t=0..20); y := t -> int(sin(t-s)*f(s),s=0..t); plot(y(t),t=0..40); g := t -> (1 - Heaviside(t-2*Pi))*t; plot(g(t),t=0..20); f := t -> sum(g(t-2*Pi*k)*Heaviside(t-2*Pi*k),k=0..20); plot(f(t),t=0..20); y := t -> int(sin(t-s)*f(s),s=0..t); plot(y(t),t=0..40); g := t -> 1 - 2*Heaviside(t-Pi) + Heaviside(t-2*Pi); plot(g(t),t=0..20); f := t -> sum(g(t-2*Pi*k)*Heaviside(t-2*Pi*k),k=0..20); plot(f(t),t=0..20); y := t -> int(sin(t-s)*f(s),s=0..t); plot(y(t),t=0..40); g := t -> 1 - Heaviside(t-Pi); plot(g(t),t=0..20); f := t -> sum(g(t-2*Pi*k)*Heaviside(t-2*Pi*k),k=0..20); plot(f(t),t=0..20); y := t -> int(sin(t-s)*f(s),s=0..t); plot(y(t),t=0..40);