- #1
prinnori
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- 0
How to Approach Oscillations Homework Problems
- Thread starter prinnori
- Start date
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Homework Help Overview
The discussion revolves around a problem related to oscillations, specifically involving the substitution of variables in equations that describe angular motion. The original poster has provided a complex equation involving trigonometric functions and is seeking assistance with their approach to solving it.
Discussion Character
- Exploratory, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- The original poster attempts to substitute variables in their equation but finds the process to be complicated. They express a need for a different approach but are unsure of what that might be.
Discussion Status
Participants are engaging with the original poster's attempts by suggesting they share their full calculations to identify any errors. Some guidance has been offered regarding simplifying the problem by ignoring higher powers and expressing certain terms in a different way, indicating a productive direction in the discussion.
Contextual Notes
The original poster has referenced an attached file containing the problem statement and equations, which may limit the ability to fully understand the context without access to that information.
- #2
tiny-tim
Science Advisor
Homework Helper
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welcome to pf!
hi prinnori! welcome to pf!
show us your full calculations, and then we'll see what went wrong, and we'll know how to help!
hi prinnori! welcome to pf!
prinnori said:
show us your full calculations, and then we'll see what went wrong, and we'll know how to help!
- #3
prinnori
- 2
- 0
θ(t)= A ( cos ωt + ε cos 3ωt );
d²θ/dt² = -ω² A (cos ωt + 9ε cos 3ωt);
θ³(t) = A³ ( cos³ωt + 3ε cos²ωt cos 3ωt + 3ε² cos ωt cos²3ωt + ε³ cos³ 3ωt ) =
= ... =
= A³/4 [ 3cos ωt (2ε²+ε+1) + cos 3ωt (3ε²+6ε+1) + 3cos 5ωt (ε²+ε) + 3ε² cos 7ωt + ε³ cos 9ωt]
Replacing all this in the equation won't help... I need a different approach but I can't think of anything else...
- #4
tiny-tim
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Homework Helper
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hi prinnori!
i] you can ignore higher powers of A and ε
ii] you need to express cos3ωt in terms of cosωt and cos3ωt (and no sin)
i] you can ignore higher powers of A and ε
ii] you need to express cos3ωt in terms of cosωt and cos3ωt (and no sin)
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