Exercises 4.8and soy(t)=±−34cos 8t−sin 8t²e−8t=54e−8tsin(8t+φ),where tanφ=(−3/4)/(−1) = 3/4andcosφ=−1<0. Thus,φ=π+ arctan(3/4)≈3.785.The damping factor is (5/4)e−8t, the quasiperiod isP=2π/8=4, and the quasifrequencyis 1/P=4/π.9.Substituting the valuesm,k= 40, andb=8√5 into equation (12) on page 213 in thetext and using the initial conditions, we obtain the initial value problem2d2ydt2+8√5dydt+40y=0,y(0) = 0.1(m)0(0) = 2 (m/sec).The initial conditions are positive to reﬂect the fact that we have taken down to be positivein our coordinate system. The auxiliary equation for this system is2r
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.