2-dimentional movement of a point

[SimpliciusH]

Ok, I know this post is not up to specs but the real problem with this is my trouble with calculus and derivatives (I'm actually worse at that than at English ;) ) in general. I only need help with this step of the homework (basic math help).

This describes the movement of the point:
x= 4*x0*cos (Angular velocity*time)
y= x0*sin (2*angular velocity*time)

Angular velocity is given as is x0.

At first I just thought dx/dt = v, and went for it by using the rule (dsink*k/dx=k*cos(k*x)) got:

Vx=-4x0*angular velocity* sin (angular velocity*t)
Vy=x0*2*angular velocity*cos (2*angular velocity*t)

I know this is wrong. Since I realized as soon as I wrote it that, angular velocity is v/r so d(v/r)/dt, trying to get through that using the rule for d(f(x)/g(x))/dx it got quickly complicated since looking at the XY graph (I got something that looks like a 8) for movment leads me to believe r is not constant.


Anyway the more basic problem is that I don't know how to solve sin (f(x)*x)/dx or the second one for cos :(

I can solve d(f(x)*x)/dx and dsin(x)/dx (since both are covered by the simple equations) but putting them together confuses the heck out of me.


You guys where very patient and helpful with my previous problem, I hope I can learn from you again. :) Again, thaks for taking the time to help a newbie with something (for you) this trivial. :)




PS I hope angular velocity is the proper english word the derivative for what I mean is dAngle/dTime its related to velocity (v= r * angular velocity).

 

[kuruman]

I know this is wrong. Since I realized as soon as I wrote it that, angular velocity is v/r...

It is not wrong. You took the derivatives correctly so the velocity components are what they are. Here you do not have circular motion, so ω=v/r does not apply. If you had circular motion then

x²+y² = constant. This is not the case here.