Inclined accelerating pendulum question

[cloughenough]

Homework Statement

A pendulum with string length L hangs inside a boxcar that is rolling down an incline at an angle Beta. The pendulum swings to a maximum angle Theta. Ignore friction, assume Beta and Theta are small.

How far from the vertical will the pendulum swing to the left while the boxcar accelerates down the incline? (in terms of Theta and Beta).

The Attempt at a Solution

I assumed that since while accelerating, the new 'rest position' would be Beta left of vertical, that the pendulum would then swing Theta to the left and right of the new rest position. Thus, it would swing Beta+Theta to the left of the vertical.

The answer says : The frame of reference has been changed. In the new reference frame, the maximum angle from the new rest position is given by Beta+Theta (<--I don't get where Beta comes from!). This is how far it will swing to either side from the rest position. This means that it will swing to the left of vertical by an amount Theta + 2(Beta).

Thank you!

 

[tiny-tim]

Welcome to PF!

Hi cloughenough! Welcome to PF!

(have a beta: β and a theta: θ )

A pendulum with string length L hangs inside a boxcar that is rolling down an incline at an angle Beta.
…
In the new reference frame, the maximum angle from the new rest position is given by Beta+Theta (<--I don't get where Beta comes from!).

As you say, you have to prove that the new 'rest position' is β to the left of vertical.

To prove that, find the x and y components (in the stationary frame) of the acceleration of the boxcar.

Then combine that with the ordinary g to give the effective acceleration … what are its x and y components?