Amplitude of small oscilliations

[funoras]

Homework Statement

http://img717.imageshack.us/img717/418/unlednsf.th.png
The amplitude of small oscilliations for the bob is x₀, and the amplitude of small oscilliations for the cart is y₀. The length of the pivot is l . What is the maximum velocity of the bob relative to the Earth ?

Homework Equations

x=x₀sin(wt)
y=y₀sin(wt)

The Attempt at a Solution

I tried taking derrivatives of the functions stated above, thus finding velocity as a function of time, and then adding those two velocity vectors using the law of cosines. (The length of the pivot is needed for finding the angle between the vectors)

 

[Rayquesto]

also remember that for angles under 15 i think degrees the way to calculate period of the pendulum is 2piesqrtL/g which means that x can=x0sin(w2piesqrtL/g)

since the same can go for the cart y=y0cos(w2piesqrtL/g)

if you derive the two, you get the equation to find the velocity of each individually

therefor dy/dt= -y0 times 2pie sqrt L/gsin(w2piesqrtL/g)
and dx/dt= x0times 2piesqrt L/g cos(w2piesqrtL/g)

find the resultant vector, plug in for L, g and w and you should get the right answer.

 

[Rayquesto]

oh and another thing you probably have to do is find the second derivative to tell you when the velocity is a maximum. I forgot about that. once you know that time plug into resultant velocity equation to get max velocity.