Driven Oscillation- Motion of a particle, with given equation.

[Self-Help]

Homework Statement

Okay.. so I have tried to do this one but no luck.

Homework Equations

w= 2 * pi* v
1/2 kA^2= 1/2mv^2 + mgh


Alright so the question:

The motion of a particle is given by x(t)= 25cm* cos 10t
What time is the kinetic energy twice the potential energy?


Not sure how to use a x(t) equation to incorporate mgh which deals motion in the y direction.

Any guide would be appreciated.. Thanks!

 

[turin]

You are probably just suffering from notational inconsistency/ambiguity. I suspect:

- The "v" in the equation for frequnecy is actually not a "v" at all, but rather Greek letter "nu". I.e., it is not velocity, but rather cyclic frequency. I would use "f" instead.

- The "x" and "y" directions are arbitrary. And so, while "y" is typically chosen to represent vertical position, "x" is just as well. In fact, you have "1/2 kA^2" and "mgh" in your energy equation, and "y" does not appear anywhere. I suspect: A=h=x in your equations.

- The equation of the motion of the particle has unitless time. I suspect that the "10" in the argument of the cosine should have some units.

BTW, why did you call this "Driven Oscillation"?

 

[Self-Help]

I just used the unit name, it's called Driven Oscillations and resonance.
Okay... hmm
so looking at it only with energy considerations... we have amplitude so we can do the equation:

1/2KA^2= 1/2 mv^2 + mv^2

... but mass shouldn't be included in the equation :S
so this is where I get stuck again!
lol ahhh