# amplitude?

• Jun 10th 2008, 07:32 AM
i_zz_y_ill
amplitude?
Given y=1/13(3sint-2cost)+e^-3t(2cost+3sint)
Q describe behaviour of y for large values of t. Sketch with range.

The amplitube is in actual fact 1/(13)^0.5

So on the graph its between -1/(13)^0.5 and 1/(13)^0.5

How can this be when the max andmin value is clearly going to be 1/13 do you think this is a typo?
I think it has something to do with the technique givenx = A sinwt=Bcoswt you can wright it as
x=(A^2+B^2)^0.5(A/<(sinwt) + B/<(cowt)) < indicates the (A^2+B^2)^0.5
But im afraid i cant see the direct relation between this straight off tchnique and the rsin(w+/-x) method or rcos(w+/-x) method is it the same thing? I dont think this is the factor formulae either!
Oh its ok i got it
• Jun 10th 2008, 05:26 PM
mr fantastic
Quote:

Originally Posted by i_zz_y_ill
Given y=1/13(3sint-2cost)+e^-3t(2cost+3sint)
Q describe behaviour of y for large values of t. Sketch with range.

The amplitube is in actual fact 1/(13)^0.5

So on the graph its between -1/(13)^0.5 and 1/(13)^0.5

How can this be when the max andmin value is clearly going to be 1/13 do you think this is a typo?
I think it has something to do with the technique givenx = A sinwt=Bcoswt you can wright it as
x=(A^2+B^2)^0.5(A/<(sinwt) + B/<(cowt)) < indicates the (A^2+B^2)^0.5
But im afraid i cant see the direct relation between this straight off tchnique and the rsin(w+/-x) method or rcos(w+/-x) method is it the same thing? I dont think this is the factor formulae either!
Oh its ok i got it

For large t: y=1/13(3sint-2cost)+e^-3t(2cost+3sint) ---> y=1/13(3sint-2cost) since e^-3t ----> 0 and (2cost+3sint) is bounded.