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Using Matlab, add plots for the following problems: 4.20 Determine the peak displacement for the impulsively excited spring-mass system, and show that it can be expressed in the form xpeak √ km Fˆ = exp − ζ √ 1 − ζ tan−1 p 1 − ζ 2 ζ ! Plot this result as a function of ζ. 4.24 The base of an undamped spring-mass system, m and k, is given a velocity pulse, as shown in attached gure. Show that if the peak occurs at t < t1, the response spectrum is given by the equation ωnzmax v0 = 1 ωnt1 − 1 ωnt1 p 1 + (ωnt1) 2 − p ωnt1 1 + (ωnt1) 2

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p=@(z) exp(-z./((1-z.^2).^0.5).*atan(((1-z.^2).^0.5)./z));
z=linspace(0.0001,.9999,100);

figure;
plot(z,p(z),'Linewidth',2);
xlabel('\zeta')...
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