Recent content by jlatshaw

The goal is to have a generic driving module that can have adjustable parameters (such as velocity and acceleration) to meet different profiles ( so I suppose the second option that you listed). But this driver won't be used for a robot arm, it will just be used for positioning (however, if you...

yes, those are the correct numbers. Here is a another plot showing when the pulses become constant and the total 'ramp up time' As far as the physical hardware, this is actually a simulation of stepper driver module that is running on a Cyclone 10 FPGA which is sending the pulses to a stepper...

Hi Berkeman, Yes, this is from a logic analyzer simulation that is counting steps from a stepper motor (each pulse is one step). And yes, the numbers on the bottom are keeping track of how many pulses have occurred. I should have mentioned that the horizontal axis is time. Also yes, my goal is...

Hello, Perhaps I am overthinking this, but I am trying to find the acceleration of the 'pulse rate' in the below plot. Every so many seconds there is a pulse (you can think of this as x displacement). The initial rate between pulses is 5 pulses/sec (you can think of this as velocity). I am...

Ok, so I figured it out: If you have a DE system that is linear, then if we know eigenvalue and eigenvectors of a coefficient matrix A, we know that trajectory plots starting at the ends of the eigenvectors will be: {x1[t_], y1[t_]} = eigenvector[1] E^(eigenvalue[1] t) {x2[t_], y2[t_]} =...

Ok, so this is a differential equation question. How can I use the eigenvectors/eigenvalues to find the formulas for straight line trajectories and from those formulas that I come up with, how can I alter them so as to start at any given point that I would like them to (like with starter data)...

Well, I want to say that: C1 Cos(5t) + C2 Sin(5t) = C1 Cos(5t) + C2 Sin(kt) and that k is just 5. Is that right to say? I'm asking this not because I have trouble determining if k = 5, but mainly to make sure I did my work correct in finding C1 Cos(5t) + C2 Sin(5t) then I know that k = 5...

oh ok. One final question regarding this. When I switch up the constants, I get C1 Cos(5t) + C2 Sin(5t) But, I'm suppose to come up with C1 Cos[5 t] + C2 Sin[k t] So what should I do about that k? Why is it not a 5? Or does k have to equal 5? Thanks. -James

Ok, I guess it's my constants that are getting me in a twist. Where am I going wrong here? knowing that: E^(ix) = cos(x) + i sin(x) and E^(-ix) = cos(x) - i sin(x) K1 E^(-5 i t) + K2 ​​E ^(5 i t) (Let x = 5t) = K1 (cos(x) - i sin(x)) + K2(cos(x) + i sin(x)) = cos(x) (K1 + K2) + i sin(x)...

Homework Statement Given: y''[t] + 25 y[t] = 0 I know that the solution to this DE is of the form: y[t] = K1 E^(-5 i t) + K2 ​​E ^(5 i t) I get that, that makes sense to me, however when I look in old DE books I see the solution to the same problem written as: C1 Cos[5 t] + C2...

So sorry! made a big bobo! I want to show: .5 * i E^(-.25 i pi t) - .5 * i E^(.25 i pi t) = Sin(pi t/4) Using the above does just that. Thanks so much! :)

Ok, so I have .5 * i E^(-.25 i pi t) - .5 * i E^(.25 i pi t) knowing: E^(i theta) = cos(theta) + i sin(theta) E^(-i theta) = cos(theta) - i sin(theta) so .5 i E^(i theta) = .5 i (cos(theta) + i sin(theta)) = .5 (i cos(theta) - sin(theta)) .5 i E^(i -theta) = .5 i (cos(theta) - i sin(theta)) =...

Ok, E^(i theta) - E^(-i theta) = 2 i sin(theta) I'm still a little bit confused as to where I can go from this. I like the way the right hand side of the equation is looking, but I don't know what to do with the imaginary component in 2 i sin(theta) Thanks, -James

I get: 2 i Sin(theta) Even still, how does that get me closer to my end? Thank you. -James

Homework Statement Hello, I am in differential equations currently and I have a homework question regarding simplifying sin( Pi t)/4 into .5 * i E^(-.25 i pi t) - .5 * i E^(.25 i pi t) Homework Equations I think they might be using Euler's Identity, but I am unsure. E^(a +...