# Need help with mass-spring-damper system

this all occurs on a horizontal plane.

a force is applied to a 2kg mass (m1). a damper is on the same side of the mass as the force and it is attached to a wall. its value is 4kg/s(b1). a spring is on the opposite side of the mass with a K value of 5(k1). the opposite end of the spring is attached to another mass of 6 kg(m2). on the other side of this mass is a spring with K of 10(k2) and a damper with a value of 4(b2). both the spring and the damper are tied to the wall. im supposed to find a differential equation that relates the output to the input and find the laplace transform of it.
the y values correspond to the position of each mass.
heres what i have so far.
for the first mass:

F = m1*y1'' + b1*y1' + k1*y1 - k2*y2

second mass:
0 = m2*y2'' + b2*y2' - k2*y2 + k1*y1

where do i go from here?

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okay, i got an answer that relates Y2 and F. numerator is 6s^2 +4s + 10
denominator is 12s^4 + 20s^3 + 66s^2 +60s +25.

i got the step response using matlab but it doesnt look quite right.

Tom Mattson
Staff Emeritus
Gold Member
I don't have time to work out the problem completely, but you should use the second equation to solve for $y_1$:

$y_1=\frac{1}{k_1}[-m_2\ddot{y_2}-b_2\dot{y_2}+k_2y_2]$,

and then differentiate twice to get $\dot{y_1}$ and $\ddot{y_1}$. Then you can sub those into the first equation and take the Laplace transform.

If that's what you did, and you don't think your answer is correct, then check your algebra.

can i get a confirmation that i analyzed the system properly? i mean as far as the beginning differential equations.

did i set up the opening differential equations right?

heres, what i got for an answer :

- 2/5 Y2 4th derivative, -32/5 Y2 3rd der. - 6/5 y2 2nd der and + 4 Y2 1st der.
is this right?