- #1
NMS2
- 1
- 0
Hello
Need some help simplifying this. In relation to a driven oscillator I am looking for wmax for which the amplitude is maximum. I understand the theory and I am just missing something with the maths and I know its probably something so stooooopid I am missing >< I'm taking the derivative but I end up with something pretty convoluted and I know this is meant to be relatively simple but I just can't get it... I am staring at it too long, need someone else to look at it.
I have worked out the Amplitude as:
A= fo/m/sqrt((wo2-w2)2+γ2w2)
Then I attempted dA/dw to get wmax for which A is max and set to zero but it all got a little out of hand
-((fo/m)(2)(wo2-w2)(-2w)+2γw2))/((2)(wo2-w2)2+γ2w2)3/2)=0
I want to work with this expression because I understand where it came from and it makes sense to me. I just can not remember how to simplify something like this and it is going to keep me awake at night
I know that its supposed to boil down to this:(but I can not get my dA/dw to look like this. )
wmax= (wo2-(γ2/2))1/2
my goal is to figure out how to make my expression look like this
>< please help
Thank you
Need some help simplifying this. In relation to a driven oscillator I am looking for wmax for which the amplitude is maximum. I understand the theory and I am just missing something with the maths and I know its probably something so stooooopid I am missing >< I'm taking the derivative but I end up with something pretty convoluted and I know this is meant to be relatively simple but I just can't get it... I am staring at it too long, need someone else to look at it.
I have worked out the Amplitude as:
A= fo/m/sqrt((wo2-w2)2+γ2w2)
Then I attempted dA/dw to get wmax for which A is max and set to zero but it all got a little out of hand
-((fo/m)(2)(wo2-w2)(-2w)+2γw2))/((2)(wo2-w2)2+γ2w2)3/2)=0
I want to work with this expression because I understand where it came from and it makes sense to me. I just can not remember how to simplify something like this and it is going to keep me awake at night
I know that its supposed to boil down to this:(but I can not get my dA/dw to look like this. )
wmax= (wo2-(γ2/2))1/2
my goal is to figure out how to make my expression look like this
>< please help
Thank you