Question

ro A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sin N (newtons) and moves in a medium that imparts a viscous force of 4 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 9 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u".) u(0) = m, u'(O) = m/s

Answer 1

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Ky = mg KX0.2 = 5X 9.8 K = 5x9.8 = 245 N/m T 0.2 External force H gan's - 10 sin (t) ody nakry = 4N = viscous force t tv = 6x2x102 = 2x102=200 (N8 m) Irosince 4 2x102 Equation of motion 10 sin (te) m m ndry -ky-Gut losinte) ata l' + t u't ku ""+you +49 u 2 sinte 40 =0 m, ul01-98152 m/s upp +40 up +490 = 2 SinLt.) Juos = [0 ]m u'0) = 10:09] m/s 2 Auswes