Simple Pendulum: Amplitude, velocity, and angular position.

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Homework Help Overview

The discussion revolves around a simple pendulum problem involving a mass of 20.0 g suspended by a 1.0 m string, raised to a height of 10.0 cm, and described by the angular position equation θ(t)=θmaxcos(ωt+∅). Participants are exploring concepts related to the period, maximum velocity, and phase constant of the pendulum.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to calculate the period and maximum velocity but expresses confusion about determining the amplitude and phase constant. They question how to derive the amplitude and what values to use in their calculations. Other participants suggest using force equations and clarify the meaning of terms like "V sub o," while also encouraging a deeper engagement with the textbook material.

Discussion Status

The discussion is ongoing, with participants providing guidance on the use of force equations and clarifying terminology. There is a mix of interpretations regarding the definitions and calculations involved, but no consensus has been reached on the specific approach to solving the problem.

Contextual Notes

Participants note the lack of detailed instruction from the professor regarding certain concepts, leading to confusion about the application of equations and definitions. The original poster emphasizes their efforts to understand the material through reading the textbook.

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Homework Statement



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A simple pendulum of mass 20.0 g is suspended by a length of string 1.0 m. It is pulled from equilibrium so that it's raised 10.0 cm and released. Angular position given by θ(t)=θmaxcos(ωt+∅)

What is the period? What is the maximum velocity of the pendulum? What is the phase constant if the mass passes through its lowest point at t=0?

Homework Equations



θ(t)=θmaxcos(ωt+∅)
v0=ωA

The Attempt at a Solution


I found T using gravity and length and am trying to get maximum velocity. My confusion stems mostly from the fact that our professor only discussed acceleration in terms of pendulums and then very briefly.

I thought that I could use v=ωA but I'm a little confused about how I'm supposed to get A for the pendulum, can I just plug in Lsinθ?

For the last part it seems to me I can just use θ=θmaxcos(∅) since t=0, but then I get caught up on what to plug in for θ. It's at its lowest point, so it seems I should simply plug in 0 and am then left with 0=θmaxcos(∅). How do I get θmax? I'm guessing this is tied into my difficulties with part 2.
 
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You need to write F = m a for the pendulum bob, remembering that there is motion in two directions. This can be done in x & y, or you can do it in r and theta (if you have talked about polar coordinates); either way should get you to the same final result.

I'm not sure what you mean by the quantity V sub o; what is your definition for this?
 
V sub o was velocity, but that is not something I'm sure of, only a wild guess based on equations in our text because our prof didn't discuss this.
 
The V almost certainly represents a velocity, but the subscript o usually denotes a particular time, often time t = 0, but not always.

I'd bet that your prof expects you to READ the book, not just look at the pictures and equations. That would be almost like listening to more lecture, and it would cover more ground. Try it; you may like it.
 
Hey man, as much as I appreciate the passive aggressive insult, I have, unbelievably, read the book. Several times, in fact. I obviously still don't understand it, which is why I went here for help.
 

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