Solving Integral Troubles with Vibrations Problem

[Saladsamurai]

Homework Statement

Alrighty. I have reduced a vibrations problem to an integral and I am having some trouble
evaluating it.

I have a value for t and need to find:$$-c\omega^2Z^2\int_0^t\cos^2(\omega t-\phi)\ dt$$ (1)I guess it is just my memory that is the problem.

If I had $\int\cos^2(x)\ dx$ It would not be a problem.

I am thinking now that I type this that a simple U substitution should do the trick right?EDIT:

If I let $u=\omega t-\phi\ \Rightarrow du=\omega\ dt$

So (1) becomes:

$$-c\omega Z^2\int_0^t\cos^2u\ du$$

Yes?

 

[lanedance]

hi - i think your limits should become u(0) & u(t) as well

 

[n!kofeyn]

If you just use the the double angle formula
[tex]\cos^2 t = \frac{1}{2} (1+\cos 2t) [/itex]
from the outset (because it's the next step after your u-substitution anyway), then you really don't need to do a u-substitution if $\omega$ and $\phi$ are just constants.

 

[haihai]

pls help me too...integration problem

hi... i am new here and i hope someone can please answer my question too..

x^-1 + dk/dy = x^-1
so when we cancel both x-1 we get dk/dy = 0

my question is can i integrate dk/dy to get the k's value??

if i integrate dk/dy, am i getting C (constant) for the k value?

thank u very much...

 

[Mark44]

Yes, if dk/dy = 0, then k = a constant.