Mass spring damper system with sinusoidal input.
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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
and three c values which equal
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.
Babak on 5 Dec 2012
You can use MATLAB's internal ODE solvers like ODE45 to solve these differential equations numerically. See
Or you could solve the differential equations using Simulink. In this case you need to create a model that represents the diffrential equations.