- #1
aerandir4
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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 that has time on the horizontal axis and f(t) on the vertical axis f(t). It goes up linearly from 0 to f(0.5)=100 and then linearly drops with negative gradient to 0 at f(1)=0 and then carries on at infinitely at f(t)=0 for t>1
The Attempt at a Solution
I think we have to define the graph first in three steps
0<t<0.5 f(t)=200t
0.5<t<1 f(t)=200(1-t)
t>1 f(t)=0
after this I'm confused on how to proceed. Initially I took each set of conditions and converted them to X(s) via laplace transforms then solved by partial fractions and then converted back to X(t). I'm not sure if this is the right method.
Another way would be to solve each condition by integration,
i.e. when 0<t<0.5 then f(t)=integral between 0 and 0.5 of exp^-st*200t dt
then substitute this value back into f(t) in the equation of motion.
some guidance would be nice.
thanks