Recent content by danj303

Think I got it. It just goes to [\alpha, \beta]

By using a linear approximation to estimate delta z so that \Deltaz = f(x0 +delta x , y0 + delta y) - f(x0,y0) But in this case I don't know delta x and y??

Thanks for the reply but sorry I don't follow you there. That is the entire question as I have written. I can understand how it works when for example you are given a parabola and have to calculate the change in height going a certain distance to one side. But in that case delta x & delta y are...

Homework Statement Compute the linearisation of z = x^\alphay^\beta about (1,1) if \alpha & \beta \neq 0. Homework Equations The Attempt at a Solution I can see how it works when \Deltax and/or \Deltay are given but not sure how to do it in this form??

Homework Statement Consider the initial value problem y'' + 1/3y' + 4y = fk(t) with y(0) = y'(0) = 0, fk(t) = 1/2k for 4 - k < t < 4 + k 0 otherwise and 0 < k < 4. (a) Write fk(t) in terms of...

I find z(t) = t e-(t-kd/v) Heaviside(t-kd/v) The only thing I am not sure about is fitting the summation back in. How do I do this??

Alright after some time I get the laplace transform of the Right hand side as e-(kd/v*s) and then sloving the entire equation for Y(s) I get Y(s) = e-(kd/v*s)/s2+2s+1 But does this take into account the sumation and then how do I take the inverse laplace transform to solve the DE

Im not sure how to take the laplace transform of δ(t-kd/v)

Im not sure about that part. Can you elaborate.

The left side is easy if you set it to equal zero. The laplace transform is s^2*Y(s) + 2s*Y(s) + Y(s) = 0 but I am not sure about the right hand side with the sum from 0 to K of the dirac delta function.

Ok that's all well and good but can you explain a little bit further. We have covered laplace transforms but only recently and I am trying to work thorugh some problems to understand how it works. Thanks

Ive got no idea where to start. Thats the problem. I would assume f(t) needs to be expressed in terms of heaviside step functions and then the differential equation solved but I am not sure.

Homework Statement The suspension system of a car is designed so that it is a damped system described by z'' + 2z' + z = f(t) where z is the vertical displacement of the car from its rest position. The car is driven over a (smooth!) road which has "catseye" embedded in the road surface...

That makes sence. So how do I go from that to solving the initial value problem??

Homework Statement Consider the initial value problem y'' + 1/3y' + 4y = fk(t) with y(0) = y'(0) = 0, fk(t) = piecewise function 1/2k if 4 - k <= t < 4 + k 0 otherwise and 0 < k < 4 (a) Sketch the graph of fk(t). Observe that the area...