- #1
prinnori
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How to Approach Oscillations Homework Problems
- Thread starter prinnori
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In summary, the conversation is about a problem involving substituting theta and finding a different approach to solve it. The person provides their attempted solution but is having trouble with the substitution. They are advised to ignore higher powers and express cos3ωt in terms of cosωt and cos3ωt in order to find a simpler solution.
- #2
tiny-tim
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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
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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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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)
- #5
rwisz
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As a scientist, it is important to approach problems in a systematic and organized manner. In this particular problem, it is helpful to first understand the physical concept of oscillations and the equations that govern them. The homework statement and equations provided in the attached file can serve as a starting point for understanding the problem.
To solve the problem, it is important to carefully read and understand the given information, including any assumptions or conditions stated. Next, it may be helpful to visualize the problem and draw diagrams or graphs to better understand the situation. From there, one can use the relevant equations and principles to set up and solve the problem systematically.
In this case, substituting theta may not be the most efficient approach. It may be helpful to first simplify the equations and use trigonometric identities to make the problem more manageable. Additionally, it may be useful to break down the problem into smaller parts and solve them separately before combining the solutions.
It is also important to check the units and ensure that they are consistent throughout the problem. Any assumptions or approximations made should also be clearly stated and justified.
Overall, approaching the problem with a logical and organized mindset, utilizing relevant equations and principles, and carefully checking the solution can lead to a successful outcome.
FAQ: How to Approach Oscillations Homework Problems
1. What is an oscillation?
An oscillation is a repetitive movement or variation between two states or positions. It can occur in various systems, such as a pendulum swinging back and forth, or a spring vibrating up and down.
2. What is the period of an oscillation?
The period of an oscillation is the time it takes for one complete cycle or back-and-forth motion. It is usually denoted by the symbol T and is measured in seconds (s).
3. How is the frequency of an oscillation calculated?
The frequency of an oscillation is the number of cycles or repetitions per unit time. It is calculated by taking the inverse of the period, so frequency = 1 / period. The unit for frequency is hertz (Hz), which is equal to 1 cycle per second.
4. What is the equation for simple harmonic motion?
The equation for simple harmonic motion is x = A sin(ωt + ϕ), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency (2π divided by the period), and ϕ is the phase constant (initial position or starting point).
5. How does the mass affect the period of a spring-mass system?
The period of a spring-mass system is directly proportional to the square root of the mass. This means that as the mass increases, the period also increases. This relationship is described by the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.