Question about a Mass-Spring-Damper

[shannonxtreme]

Homework Statement

1) The schematic diagram for the suspension system at one corner of a road vehicle is shown below. The displacement of the road wheel is denoted x, and the resultant displacement of the vehicle body is y.
IMAGE - http://imgur.com/VxKx5Qq
Values of the spring rate, k, damping coefficient, c, and mass, m, are given below.
k - 7 x 10⁴ N/m
c - 3 x 10³ N/m/s
m - 250 kg
Analysis / Modelling
a) Develop a Laplace Transform model of the system and use this to predict the displacement, y, in response to various inputs, x, (e.g., step, impulse, ramp).

Can anyone help me solve this? It has been a while and I am very rusty indeed.

 

[Hesch]

Develop a Laplace Transform model of the system

Sketch a diagram as shown below:

Well, it's not a mass-spring-damper system, but some electric motor.

Anyway, you should get something like that, with one or more closed loops.

Now, use Mason's rule to reduce the diagram to a transfer function: y(s)/x(s) = numerator / denominator.

Set the input, x(s) = ramps/sine waves/whatever, multiply by the transfer function, and you will get the response, y(s).

Job done.

 

[Chestermiller]

If x is the upward displacement of the axle and y is the upward displacement of the mass, what is the tension in the spring as a function of x and y? What is the force of the damper as a function of the time derivatives of x and y? What is the Newton's law force balance on the mass in terms of x and y, and their first and second time derivatives?

Chet