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AbigailM
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After finding the equations of motion of a pendulum in an accelerating cart:
[itex]\ddot{\phi} + \frac{acos\phi +gsin\phi}{l}=0[/itex]
,the method that Taylor uses in Prob 7.30 for finding the small angle frequency, is to rewrite [itex]\phi[/itex] as [itex]\phi_{0}+\delta \phi[/itex]. Then you can use a trig identity in the equation of motion to get the frequencies.
My question is what is the reasoning for rewriting [itex]\phi[/itex] the way we do?
To me it looks like just the amplitude since [itex]\phi_{0}[/itex] is just the angle that the pendulum makes with the normal when it is at rest relative to the cart.
Thanks.
[itex]\ddot{\phi} + \frac{acos\phi +gsin\phi}{l}=0[/itex]
,the method that Taylor uses in Prob 7.30 for finding the small angle frequency, is to rewrite [itex]\phi[/itex] as [itex]\phi_{0}+\delta \phi[/itex]. Then you can use a trig identity in the equation of motion to get the frequencies.
My question is what is the reasoning for rewriting [itex]\phi[/itex] the way we do?
To me it looks like just the amplitude since [itex]\phi_{0}[/itex] is just the angle that the pendulum makes with the normal when it is at rest relative to the cart.
Thanks.
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