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Advanced Physics Homework Help
Solving for Normal Modes in a Non Similar Coupled Pendulum
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[QUOTE="TSny, post: 4534325, member: 229090"] Hello. OK, so you have two coupled differential equations: m1*a1=-m1*g*(x1/l)[COLOR="Red"][B]-[/B][/COLOR]kΔx m2*a2=-m2*g*(x2/l)[COLOR="red"][B]-[/B][/COLOR]kΔx I think you have one sign error in these equations if Δx stands for the same quantity in both equations. (You didn't state what Δx means. [COLOR="DarkSlateGray"][B]Correction[/B][/COLOR]: You did state that Δx is x[SUB]1[/SUB]-x[SUB]2[/SUB]. Can you see which of the equations has a sign error?) If the spring exerts a negative force on one of the masses, will it also exert a negative force on the other mass? You're going to try to find normal mode solutions in the form x[SUB]1[/SUB] = A[SUB]1[/SUB]cos(ωt + ##\phi##) x[SUB]2[/SUB] = A[SUB]2[/SUB]cos(ωt + ##\phi##) Rather than add the two differential equations, try solving them simultaneously for A[SUB]1[/SUB] and A[SUB]2[/SUB] and see what happens. [/QUOTE]
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Solving for Normal Modes in a Non Similar Coupled Pendulum
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