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 seperately...

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.