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B Simple harmonic motion in an accelerating car

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  1. Apr 12, 2017 #1
    There's a pendulum attached to a car accelerating with ##A##. I know I can find it's time period using the "effective" g method, but I want to find it from first principles.

    My attempt:
    ##tan\theta = A/g##
    Now I displace it by ##\alpha## giving ##mgsin(\theta+\alpha)-mAcos(\theta+\alpha) = ma##

    Expanding this and using small angle approximations:

    ##gsin\theta+g\alpha cos\theta-Acos\theta + A\alpha sin\theta = a##

    Where did I go wrong?
     
  2. jcsd
  3. Apr 12, 2017 #2

    Ibix

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    Can you simplify your last equation with your first? Does the result look like ##\ddot\alpha\propto-\alpha##? If so, is the constant of proportionality what you expect from doing it the easy way? Is its sign right?
     
  4. Apr 12, 2017 #3
    You also need to express a as a function of α.
     
  5. Apr 12, 2017 #4
    I got it. Thanks!
     
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