How Do You Solve These Multivariable Calculus Problems Related to a Helix?

[pezzang]

Hey, I need your help doing some of math problems.

Q) A particle's position at time t is determined by the equation of the helix

r(t) = < cost, sint, t>

Let P be a point with a coordinates (0,1,pie/2).

1. Find the curvature k(t) at any time t.


2. Find the center of the osculating circle at P.


3. Write down the equation of the osculating plane and the sphere whose intersection with that plane is the osculating circle.

4. Find a parametric equation of the osculating circle at P.

5. Find the acceleration normal vector and tangential acceleration tension vector components of the acceleration vector at P.

If any of you can do these problems, I would appreciate your help. I started finding curvature but i didn't know how to find the curvature with just the vector equation. I thought i needed y = f(x) equation to find curvature. Can anybody answer this by doing number 1 and so on?

Thank you so much in advance!

 

[mathwonk]

sir, you got no responses to this. I apologize for our lack of interest. The reason is your request is essentially for someone to do your work for you. try asking things differently. try asking for an explanation of what is going on. or asking for a simpler problem, or something that invovles your doing some of the work, not asking us to do it for you. for give me, i hope this is useful in future.

 

[Math Is Hard]

Sir? Could be a ma'am.

 

[mathwonk]

in that case my apologies to ms pezzang.