A pendulum inside an oscillation railroad car.

[anban]

Homework Statement

A pendulum length l is suspended inside a railroad car. The railroad car is oscillating so that its suspension has position xs = A cos (ωt) and ys= 0. Use the angle $\varphi$ as the generalized coordinate and write down the equations that give the Cartesian coordinates of the bob in terms of $\varphi$ and vice versa.

This is also problem 7.11 in Taylor's Classical Mechanics text.

The Attempt at a Solution

By geometry, thinking of the x and y direction separately...

x= lsin$\varphi$ + Acosωt
y= lcos$\varphi$

This gives the Cartesian coordinates in terms of $\varphi$.

But how do I give the $\varphi$ component in terms of x and y? Do I just solve for $\varphi$?

 

[BruceW]

looks good so far. One thing to watch out for: are you defining phi as "pointing straight up" or "pointing straight down" and is y going to represent "up" or "down" ?
And yep, just solve for phi. Hint: or at least, solve for some trigonometric function of phi.