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Homework 11 Solution

# 100 n m means dtdx 0 noting that dtdx dtdh we wish

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Unformatted text preview: scillator 12ghlustgated in Figures as il r 15.21 and 15.22. Assume the mass is 375 g, the spring constant to ﬁnd xN/m,thatd is a maximum,swhich(a) How 0.100 N /m. means dT/dx = 0. Noting that dT/dx = −dT/dh, We wish is 100 such an T b long does it takes for the amplitude to drop to half its initial value? (b) What If? How long doesdT take dTr the it fo =− =0 (8) mechanical energy to drop to half its dx itial dh lue? in va (c) Show that, in general, the fraction2 l rate at which the 1a l + h2 d 12armoni oscillator is amplitude decreases in a damped h c =0 2π (9) dh gh half the fractional rate at which the mechanical energy −1/2 decreases. 12 2 1 −l2 1 12 l + h 2o (10) 71. A block π f mass m is c2 + onnected to two springs o=f0 f orce con2 12gh g gh stants k 1 and k 2 as shown in Figures P15.71a and P15.71b. −l2 1 In each case, the block moves=⇒ a frictionless t= 0 after it on + able (11) 2 12gh is displaced from equilibrium and released. g how that in S the two cases the block exhibits simple h12h2 = l2 motion armo...
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