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A pendulum inside an oscillation railroad car.

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data

    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 [itex]\varphi[/itex] as the generalized coordinate and write down the equations that give the Cartesian coordinates of the bob in terms of [itex]\varphi[/itex] and vice versa.

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

    3. The attempt at a solution

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

    x= lsin[itex]\varphi[/itex] + Acosωt
    y= lcos[itex]\varphi[/itex]

    This gives the Cartesian coordinates in terms of [itex]\varphi[/itex].

    But how do I give the [itex]\varphi[/itex] component in terms of x and y? Do I just solve for [itex]\varphi[/itex]?
     
  2. jcsd
  3. Jan 29, 2013 #2

    BruceW

    User Avatar
    Homework Helper

    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.
     
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