between 0<t<0.5
i plugged in 200t=kx+c(dx/dt)
now---> 200/s^2=kX(s)+c[sX(s)-X(0)]
I re arranged in terms of X(s)=200/s^2*(k+cs)
after using partial fractions i get X(s)=-1/40s+1/50*s^2+1/40*(k/c+s)
which would give X(t)=-1/40+t/50+exp^(-k/c*t)/40
doing the same for 0.5<t<1
I get...
Homework Statement
Spring-Damper system has a force applied such that the formula f(t)= kx(t)+c(dx/dt) holds
Determine the resulting displacement x(t) and sketch the function.
What is the displacement at t=1 sec?
Homework Equations
k=10^4 Nm^-1
c=1.25x10^4 Nsm^-1
x(0)=0
the is also a graph...
im getting a little confused now :confused:
I don't understand why its as^2+bs+c=a(s-s1)(s-s2).
Is this a special case or something? I have never seen it done like that before
at this stage... s1,s2=-6/5+-12i/5
don't you just take the whole term on the right to the left hand side...
I can't see how I've gone wrong. If you use the quadratic formula straight up with
a=1.25, b=3 and c=9 then
s1,s2=-3+-sqrt(9-45)/(5/2)
s1,s2=-3+-sqrt(-36)/(5/2)
s1,s2=-3+-6i/(5/2)
s1,s2=-6/5+-12i/5
so s+6/5-12i/5 and s+6/5+12i/5 are the two roots
Homework Statement
expand by partial fractions:
Homework Equations
2(s+5)/(1.25*s^2+3s+9)
The Attempt at a Solution
ok I initially used the quadratic formula to get the two roots for the denominator
these being
(s+6/5+12i/5)(s+6/5-12i/5) i.e complex numbers
so now the partial fractions...