# Mass spring damper system with sinusoidal input.

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Christopher LaBorde on 5 Dec 2012
I am trying to solve a problem in which I am given the values
p = 5
q = 8
r = 3
From these values I must find three separate k values which equal
(p,q,r)/150 N/m
and three c values which equal
(p,q,r)/800 kg/s
For my springs and dampers. My mass is simply 5 grams, and my sinusoidal input is
y(t) = 0.008sin(9t) m
The objective is to find which spring and damper configuration will work within the specified limits below.
The mass is placed in a protective housing, making it so that the difference between its input (y(t)) and resulting x(t) cannot exceed zmax, which is given as 33.6mm, and the force transmitted to the base housing cannot exceed 1.67 mN.
I have reasoned that the representative equation to model this is
z = y - x
z' = y'-x'
mx''+cx'+kx = cy'+ky
Being the equation of motion,with my y and y' values already known. and
Ft = c(y'-x')+k(y-x)
For the transmitted force of the moving mass.
I am having issues solving for x and plotting the displacement z to see which values work within the given zmax and Fmax values.
Any help would be greatly appreciated.
Thanks.

Babak on 5 Dec 2012
You can use MATLAB's internal ODE solvers like ODE45 to solve these differential equations numerically. See
doc ODE45
for example.
Or you could solve the differential equations using Simulink. In this case you need to create a model that represents the diffrential equations.
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Babak on 6 Dec 2012
What is dsolve? Is it in the Symbolic Math Toolbox?
What problem do you have using it then?