
#1
January 17th, 2020,
23:41
HELP!!!!
totally lost and confused with this question:
A machine is subject to two vibrations at the same time.
one vibration has the form: 2cosÏ‰t and the other vibration has the form: 3 cos(Ï‰t+0.785). (0.785 is actually expressed as pi/4)
determine the resulting vibration and express it in the general form of: n cos(Ï‰t±Î±)

January 17th, 2020 23:41
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#2
January 18th, 2020,
11:49
Originally Posted by
jenney
HELP!!!!
totally lost and confused with this question:
A machine is subject to two vibrations at the same time.
one vibration has the form: 2cosÏ‰t and the other vibration has the form: 3 cos(Ï‰t+0.785). (0.785 is actually expressed as pi/4)
determine the resulting vibration and express it in the general form of: n cos(Ï‰t±Î±)
$2\cos(\omega t) + 3\cos \left(\omega t + \dfrac{\pi}{4} \right)$
$2\cos(\omega t) + 3\left[\cos(\omega t)\cos\left(\dfrac{\pi}{4}\right)  \sin(\omega t)\sin\left(\dfrac{\pi}{4}\right)\right]$
$2\cos(\omega t) + \dfrac{3\sqrt{2}}{2}\left[\cos(\omega t)  \sin(\omega t)\right]$
$\dfrac{4+3\sqrt{2}}{2}\cos(\omega t)  \dfrac{3\sqrt{2}}{2}\sin(\omega t)$
note $A\cos{x} + B\sin{x} = R\cos(x  \alpha)$, where ...
$R = \sqrt{A^2+B^2}$ and $\alpha = \arctan\left(\dfrac{B}{A}\right)$
... see what you can do from here. Note that the values for $R$ and $\alpha$ are not "nice".