Question

(1) Write an initial value problem for the displacement u(t) of a spring system with mass m=8, spring constant k=19, and dampening γ=5, which begins at position −1 with velocity −3.

(2) Solve this differential equation and plug in the initial values to get a formula for the position of the mass at time t.

Answer 1

m x'' + b x' + k x =0

Answer 2

plug your number in and solve differential equation

Answer 3

i found the differential equation as 8u^2+5u+19=0

Answer 4

and then initial values of u(0)= -1 , u'(0)=-3

Answer 5

i put the initial values and found u(t)=-exp(-0.3125t)*cos(1.50909)-1.98*exp(-0.3125t)*sin(1.50909)

Answer 6

yes but webwork doesn't accept it and the values are kinda complicated

Answer 7

You are missing t in your sine and cosine

Answer 8

i tried it now and it still doesn't accept it

Answer 9

Try this

Answer 10

\[y[t]\to -\frac{1}{11} e^{-5 t/16} \left(11 \text{Cos}\left[\frac{\sqrt{583} t}{16}\right]+\sqrt{583} \text{Sin}\left[\frac{\sqrt{583} t}{16}\right]\right)\]

Answer 11

thanks so much but it didn't work

Answer 12

-1/11e^(-5t/16)((11*cos(sqrt(583)/16)t+sqrt(583)*sin(sqrt(583)/16)t))
if i wrote it truly though

Answer 13

it did work,sensei. i think i put some extra paranthesis when writing it. thanks