Question

SPRING MASS PROBLEM!
1/5x'' +1.2x'+2x=5cos(4t), x(0)=1/2, x'(0)=0

a) Explin what every variable, constant and IC represents in the system
b)Is the system forced/unforced?
c)Is the system damped/undamped?
d) What behaviour would you expect from this system?

Answer 1

y=yh+yp
\[\frac{ 1 }{ 5 }x''+1.2x'+2x=5\cos(4t)\\x'' +6x10x=25\cos(4t)\\t^2+6t+10=0\\t=\frac{ -6\pm \sqrt{36-100} }{ 2 }=-3\pm4i\\yh=e^{-3t}(a \cos 4t+ b \sin (4t) )\\yp=c \cos (4t) +d \sin(4t)\\\]

Answer 2

now apply initial condition to find y

Answer 3

hi, before solving the IVP, I'm trying to understand it. I understand the parts of the equation, but I still cannot see how the system behaves. Do you mind explaining to me how it behaves as t increases?

Answer 4

you find variables ?

Answer 5

You have to find variables? Can you determine how the system behaves just by looking at the equation alone?

Answer 6

i think
finding var. are useful to graph behavior of system
then describe it

Answer 7

hmmm.. ok i'll try that. Thanks