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