Question

ITEMS JIIMARY 3. < Previous Ne A mass of 10 kg stretches a spring 14 cm. The mass is acted on by an external force of 4 sin(t/3) N and moves in a medium that imparts a viscous force of 3 N when the speed of the mass is 6 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 2 cm/s, determine the position u of the mass at any time t. Use 9.8 m/s² as the acceleration due to gravity. Pay close attention to the units. u(t) = m

Answer 1

To solve this question you must need to understand these concepts -

1 . spring-mass oscillation concepts.

2. knowledge of linear diffferential equation of 2nd order.

3. basic knowledge of differentiation and integration.

solution Given that m = 5kg L = 14-cm 0.14m L = 0.14.m F(t) = 431n/H3) N fv = -3N U(+)- 6 cm = 0.06 mix 410) om ulo) = 2(M = 0.02 m/ from fa kn (x = 2 ] f mg L 5 x 9.81 0.14 350 kg / 5² from Fv=-7 ult) twe have

o=&tiß = -333 = 7.675 x = eat a cap But + Bringa] (x = -3:33 ß = 7.675) 4 5 P-I = T (D?+6-66D +70) 몰 7 4 ** (13) 1776660+70 4 3 0,11 +6-66D+70 . 4 5 famlt13) 6.66D + 700ll 6.66D-70111 6:66 0² (10.11)² 5 6.66D-70.11) I fin (1/3) (6.66x0111 -7011) (4 66 D -7 (1) gin (1/3) 5x69.3

=-0.011[6.66 Cop (118) - 70111 Bini (1/3) P.I = -0.011 [P-2268 (4/3) - 7o11 pin (1/3)] y='cft P.I x = c.ft.P.I X (t) or ult) eat (ACABA + B sin ßt] + -1011 12.22.07 (ts) - 70.11 pinta) eft)= ett faconßt + B sinBt] p=0.011( 2: 22 COM(+13) ) - 70.1) go ( 413)] d=-3.33, B = 71675 4(0)-0, ulo) = 0,02 m