Spring and string pendulum (oscillations)

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The discussion revolves around a pendulum affected by a spring, focusing on the equations of motion and oscillation characteristics. The participants analyze the motion using small angle approximations and derive the equation of motion, which incorporates both spring and gravitational forces. They explore the equilibrium position and angular frequency, with ongoing clarifications about initial conditions and the role of various forces. Key points include the need for correct sign conventions in the equations and the interpretation of the pendulum's motion as it oscillates around its equilibrium position. The conversation highlights the complexities of deriving accurate motion equations in oscillatory systems.
  • #31
JulienB said:
@haruspex I imagine so since it was a problem at a real exam a couple of years ago. Well I read the problem again and nothing's stated about t=0 until question c) and it is unfortunately for α = 0 then.
Yes, my remark about t=0 was only in relation to part c.
For part b, the only other suggestion I have is that it should say to find αR in terms of m, L, k and x0.
 
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  • #32
Also, if I assume that α(0) = αR, I think it implies that B = 0.
 
  • #33
haruspex said:
Yes, my remark about t=0 was only in relation to part c.
For part b, the only other suggestion I have is that it should say to find αR in terms of m, L, k and x0.

Yes and that could be easily done with the force equation right? Well, thank you for your help in any case! Was my reasoning in part c) coherent?Julien
 
  • #34
JulienB said:
Yes and that could be easily done with the force equation right? Well, thank you for your help in any case! Was my reasoning in part c) coherent?Julien
In the equation you posted for α'(0) you had a sign wrong, but that must have been a mistake in typing the post since the answer you got is right.
 
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