# Response Function for a Damped, Linear Oscillator

#### piano.lisa

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:
S

#### SGT

##### Guest
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?

#### piano.lisa

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.

S

#### SGT

##### Guest
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

Last edited by a moderator:

#### piano.lisa

Last edited by a moderator:

#### piano.lisa

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)?

http://www.oksana-design.com/response_function_p1.jpg" [Broken]
http://www.oksana-design.com/response_function_p2.jpg" [Broken]

Last edited by a moderator:
S

#### SGT

##### Guest
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)?

http://www.oksana-design.com/response_function_p1.jpg" [Broken]
http://www.oksana-design.com/response_function_p2.jpg" [Broken]
There is an alternate way to find the response. Are you familiar with the step function u(t)?

Last edited by a moderator:

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