Determining an object's velocity in cylindrical coordinates

[Marcis231]

Homework Statement

An object in motion all the time is represented by the equation
r = a cos (bt + c) i + a sin (bt + c) j + et k With a, b, c, e are constant. Determine the velocity equation and the object's acceleration equation as a function of time and graph the shape of the particle's motion over time.

Relevant Equations

r = a cos (bt + c) i + a sin (bt + c) j + et k

I got the answer for velocity and acceleration. But I don't know how to draw the shape of the particle's motion over time. How to draw it? should we change a,b,c,e into a numbers or not? or we may not to change a,b,c,e?
Please help me how to draw the shape of particle's motion over time?

 

[Marcis231]

I got the answer for velocity and acceleration. But I don't know how to draw the shape of the particle's motion over time. How to draw it? should we change a,b,c,e into a numbers or not? or we may not to change a,b,c,e?
Please help me how to draw the shape of particle's motion over time?

 

[Master1022]

One thing I would do is to just consider the motion in the plane for the moment. That is, what is the shape drawn out in the i and j directions? We have a cosine in the $\hat i$ (i.e. x) direction and a sine in the $\hat j$ (i.e. y direction). What shape is parameterised by $x = r cos(\theta)$ and $y = r sin(\theta)$? Once you know that, then you can think about the effect of the $\hat k$ component. As time $t$ increases, what happens to the size of $et$?

I hope that provides a place to start

 

[vanhees71]

I guess you should just draw the trajectory qualitatively. To get an idea, first think about the special case $e=0$. What curve do you get then? Then think about what $e \neq 0$ does in addition to the special case!