Exam (elaborations) TEST BANK FOR System Dynamics 3rd Edition By William J. Palm III (Solution Manual)-Converted

1.1 W = mg = 3(32.2) = 96.6 lb. 1.2 m = W/g = 100/9.81 = 10.19 kg. W = 100(0.2248) = 22.48 lb. m = 10.19(0.06852) = 0.698 slug. 1.3 d = (50 + 5/12)(0.3048) = 15.37 m. 1.4 d = 3(100)(0.3048) = 91.44 m 1.5 d = 100(3.281) = 328.1 ft 1.6 d = 50(3600)/5280 = 34.0909 mph 1.7 v = 100(0.6214) = 62.14 mph 1.8 n = 1/[60(1.341× 10−3)] = 12.43, or approximately 12 bulbs. 1.9 5(70 − 32)/9 = 21.1 C 1.10 9(30)/5+ 32 = 86 F 1.11 ! = 3000(2)/60 = 314.16 rad/sec. Period P = 2/! = 60/3000 = 1/50 sec. 1.12 ! = 5 rad/sec. Period P = 2/! = 2/5 = 1.257 sec. Frequency f = 1/P = 5/2 = 0.796 Hz. 1.13 Speed = 40(5280)/3600 = 58.6667 ft/sec. Frequency = 58.6667/30 = 1.9556 times per second. 1.14 x = 0.005 sin 6t, x˙ = 0.005(6) cos 6t = 0.03 cos 6t. Velocity amplitude is 0.03 m/s. ¨x = −6(0.03) sin 6t = −0.18 sin 6t. Acceleration amplitude is 0.18 m/s2. Displacement, velocity and acceleration all have the same frequency. 1.15 Physical considerations require the model to pass through the origin, so we seek a model of the form f = kx. A plot of the data shows that a good line drawn by eye is given by f = 0.2x. So we estimate k to be 0.2 lb/in. c 2013 McGraw-Hill. This work is only for non-profit use by instructors in courses for which the textbook has been adopted. Any other use without publisher’s consent is unlawful. 1.16 The script file is x = [0:0.01:1]; subplot(2,2,1) plot(x,sin(x),x,x),xlabel(0x (radians)0),ylabel(0x and sin(x)0),... gtext(0x0),gtext(0sin(x)0) subplot(2,2,2) plot(x,sin(x)-x),xlabel(0x (radians)0),ylabel(0Error: sin(x) - x0) subplot(2,2,3) plot(x,100*(sin(x)-x)./sin(x)),xlabel(0x (radians)0),... ylabel(0Percent Error0),grid The plots are shown in the figure. 0 0.5 1 0 0.2 0.4 0.6 0.8 1 x (radians) x and sin(x) x sin(x) 0 0.5 1 −0.2 −0.15 −0.1 −0.05 0 x (radians) Error: sin(x) − x 0 0.5 1 −20 −15 −10 −5 0 x (radians) Percent Error Figure : for Problem 1.16. From the third plot we can see that the approximation sin x  x is accurate to within 5% if |x|  0.5 radians. c 2013 McGraw-Hill. This work is only for non-profit use by instructors in courses for which the textbook has been adopted. Any other use without publisher’s consent is unlawful. 1.17 For  near /4, f()  sin  4 + cos  4  −  4  For  near 3/4, f()  sin 3 4 + cos 3 4  − 3 4  1.18 For  near /3, f()  cos  3 − sin  3  −  3  For  near 2/3, f()  cos 2 3 − sin 2 3  − 2 3  1.19 For h near 25, f(h)  p25 + 1 2p25 (h − 25) = 5 + 1 10 (h − 25) 1.20 For r near 5, f(r)  52 + 2(5)(r − 5) = 25 + 10(r − 5) For r near 10, f(r)  102 + 2(10)(r − 10) = 100 + 20(r − 10) 1.21 For h near 16, f(h)  p16 + 1 2p16 (h − 16) = 4 + 1 8 (h − 16) f(h)  0 if h −16. c 2013 McGraw-Hill. This work is only for non-profit use by instructors in courses for which the textbook has been adopted. Any other use without publisher’s consent is unlawful. 1.22 Construct a straight line the passes through the two endpoints at p = 0 and p = 900. At p = 0, f(0) = 0. At p = 900, f(900) = 0.002p900 = 0.06. This straight line is f(p) = 0.06 900 p = 1 15, 000 p 1.23 (a) The data is described approximately by the linear function y = 54x − 1360. The precise values given by the least squares method (Appendix C) are y = 53.5x− 1354.5. (b) Only the loglog plot of the data gives something close to a straight line, so the data is best described by a power function y = bxm where the approximate values are m = −0.98 and b = 3600. The precise values given by the least squares method (Appendix C) are y = 3582.1x−0.9764. (c) Both the loglog and semilog plot (with the y axis logarithmic) give something close to a straight line, but the semilog plot gives the straightest line, so the data is best described by a exponential function y = b(10)mx where the approximate values are m = −0.007 and b = 2.1 × 105. The precise values given by the least squares method (Appendix C) are y = 2.0622× 105(10)−0.0067x. c 2013 McGraw-Hill. This work is only for non-profit use by instructors in courses for which the textbook has been adopted. Any other use without publisher’s consent is unlawful.