- #1

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## Homework Statement

Hi. The problem is question 1(a) in the file below:

http://www.mth.uct.ac.za/Courses/MAM24678/mod2od/Project1_07.pdf

## The Attempt at a Solution

Question 1(a) is the one I have a problem with. I just don't know what he's getting at. Is y(x) the function that describes the road? And comparing y(t) and y(x) implies, to me, that x=vt, so it has a constant velocity with respect to the x-axis; a very odd thing to do...

Is Y then the vertical displacement of the vehicle from the x-axis? So the car is like a mass on a spring ,on the road? I have no idea how he derived that Differential Equation.

Please, any help on deriving the differential equation would be great

Any help is much appreciated thanks.

(P.S. I need this pronto please !)

Ok, what I did. First I said:

Y = y + p + l

l is the relaxed length of the spring (a constant), and p is the displacement from the equilibrium position of the mass on the spring. If you re-write:

p = Y - y - l

then find the equation of motion of the mass on the spring:

m[d^2(p)]/dt^2 = -kp -c(dp/dt)

And plugging in p = Y - y -l, but this does not give the correct answer. I really do not know how to get the differential equation, help please!