Question

Please solve the problem below. I would really like to see work shown so I can understand the concepts and the things I am doing incorrectly.

|(1 point) A mass of 4 kg stretches a spring 40 cm. The mass is acted on by an external force of F(t) = 97 cos(0.5t) N and moves in a medium that imparts a viscous force of 4 N when the speed of the mass is 8 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 6 cm/s, formulate the initial value problem describing the motion of the mass. Note that the acceleration due to gravity, g, is g = 980 cm/s2 Find the general solution to your differential equation from the previous part. Use C1 and C2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. eA-(1/16) C1"sin(sqrt(6271/4)/8 t) e^-(1/16)"C2"cos(sqrt(6271/4)/8 "t) Solve the differential equation with initial conditions describing the motion/the displacement y(t) of the mass from its equilibrium position. y(t) = cm

Answer 1

Sol:- (d) Considethe Given IvP 91 Cos o.st) 4y +0 5y't 98y Wrth y co)= amd The chovacterChic f's eaton Amto m +98 =6 -o-5t C+) 204) - 1569. 15 VI56.15 he comemmiavy olution is Coc (.q41t Partculav Colutio o Let The Cos Co-St) 4-bt0.5 Dt 98 Co) Replace 4C Co 5 +6.5D9391 cos (o.5t)) ян сос (о.st). 91to.5D Murtiply amd Divide by (91 -05 D)

(o-5t)) 91-O.5D Cat COS 9Co-5 (a4) tCo.5) (9S8th Cos C0-st) afain Rephu by - Co. J Cos Co. st) 48.51 2. 48.5D Cos Co.5t) + 0 125 CDst)) O.5 Sin 901-48.5 9409.125 SinCo st) 9401- 125 The Gemera Soluto is y- typ C4-141)t Cos C2 Sin 4.Y9E Cost)) t24. 25 Sin 7407.1L (7409 Sin4741)) (u.14 C4.949t COS 4.941 t 4-949 Cos

(e) Initial blition OSe Lohb 9409. 15 9409 าาาาา 9409- 125 and 'co) 6 9409 1409 t6 (9409-I5) 4.949 4.949 (4-941t)1T11 Sin 6. 9999 COS Thuufore .4t (o 9199 to.025T73 Sin Co-5t))