Response Function for a Damped, Linear Oscillator

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Homework Help Overview

The discussion revolves around finding the response function for a damped linear oscillator subjected to a specific forcing function. The original poster describes initial conditions and the nature of the forcing function, which includes a ramp and a step function. There are concerns regarding the interpretation of the step function and how to approach the problem given the limitations of the textbook.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the nature of the forcing function and its implications for finding the response function. Questions arise about the treatment of ramp functions and the definition of the step function. Some participants express confusion over the lack of clarity in the textbook and seek guidance on how to start the problem.

Discussion Status

There is an ongoing exploration of the problem with participants sharing their interpretations and seeking clarification. Some guidance has been offered regarding the nature of the forcing function, but there is no explicit consensus on how to proceed. The original poster has expressed a need for further assistance and clarification on specific aspects of the problem.

Contextual Notes

Participants mention the inadequacy of their textbook in addressing response functions and the absence of references to ramp functions, which adds to the complexity of the discussion. There are also mentions of needing to transcribe problems for better understanding.

piano.lisa
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I have a damped linear oscillator, originally at rest in its equilibrium position [therefore, x(0)=0 and x'(0)=0]. It is subjected to a forcing function:
F(t)/m =
{0, if t<0
{a(t/tau), if 0<t<tau
{a, if t>tau

I have to find the response function. However, when I attempt to find the step function H(t), I will end up with 0 as my constants [because of the a(t/tau) when t=0], therefore, saying that there is no step function.
The textbook and my lecture notes are not great aids at solving this problem. Please provide me with any tips to getting started, or any useful websites.

Thank you.
 
Last edited:
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piano.lisa said:
I have a damped linear oscillator, originally at rest in its equilibrium position [therefore, x(0)=0 and x'(0)=0]. It is subjected to a forcing function:
F(t)/m =
{0, if t<0
{a(t/tau), if 0<t<tau
{a, if t>tau

I have to find the response function. However, when I attempt to find the step function H(t), I will end up with 0 as my constants [because of the a(t/tau) when t=0], therefore, saying that there is no step function.
The textbook and my lecture notes are not great aids at solving this problem. Please provide me with any tips to getting started, or any useful websites.

Thank you.
Your forcing function is a ramp between 0 and tau and a step for t > tau. A ramp is 0 for t = 0. I don´t see what is your problem.
How are you trying to calculate the response function?
 
The true problem is the fact that we weren't properly taught response functions and our textbook is lacking.
Therefore, by following the example in the textbook, I simply get x(t) = 0.
What I really need here is not only help, but a quick tutorial.

How do you start a problem about finding the response function?
There is no reference to "ramps" in the textbook, so I don't know how to treat them in the response function. The only thing in the textbook is the step function.
 
piano.lisa said:
The true problem is the fact that we weren't properly taught response functions and our textbook is lacking.
Therefore, by following the example in the textbook, I simply get x(t) = 0.
What I really need here is not only help, but a quick tutorial.

How do you start a problem about finding the response function?
There is no reference to "ramps" in the textbook, so I don't know how to treat them in the response function. The only thing in the textbook is the step function.
There is no way to help you if we don't know what the problem is. Could you transcribe the text of your problem and the example in your textbook?
 
jalaldn said:
http://id.mind.net/~zona/mmts/functionInstitute/functionInstitute.html
http://www.ima.umn.edu/~arnold/graphics-g.html

I'm sorry, but those links were of no help.

SGT: I will scan the long question later tonight.

Any other help is strongly appreciated. I really need it!
 
Last edited by a moderator:
Attached are what I have done for the question so far. I have found the Response function for each condition. However, in order to find the "response" that the professor will be looking for, do I have to find the impulse to the response function?
If so, how can I achieve this? Do I take x(t) = H(tau) - H(t) - H(0) ? Also, which response function do I use for each of H(tau), H(t), and H(0)?

Please answer as soon as possible. Thank you.

http://www.oksana-design.com/response_function_p1.jpg"
http://www.oksana-design.com/response_function_p2.jpg"
 
Last edited by a moderator:
piano.lisa said:
Attached are what I have done for the question so far. I have found the Response function for each condition. However, in order to find the "response" that the professor will be looking for, do I have to find the impulse to the response function?
If so, how can I achieve this? Do I take x(t) = H(tau) - H(t) - H(0) ? Also, which response function do I use for each of H(tau), H(t), and H(0)?

Please answer as soon as possible. Thank you.

http://www.oksana-design.com/response_function_p1.jpg"
http://www.oksana-design.com/response_function_p2.jpg"
I have already answered to your private message.
There is an alternate way to find the response. Are you familiar with the step function u(t)?
 
Last edited by a moderator:
Thanks for your help SGT.
 

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