I have the vector:
{\bf{u}}(x,y) = \frac{{x{\bf{i}} + y{\bf{j}}}}{{{x^2} + {y^2}}}
Where:
x = a\cos t y = a\sin t
I know I need to use the equation
\int\limits_0^{2\pi } {{\bf{u}} \cdot d{\bf{r}}}
And the answer is
\int\limits_0^{2\pi } {} ((a\cos t/{a^2})( - a\sin t) +...
But I guess that this equation links amplitude and the frequency?
\begin{array}{l}
A = \frac{P}{{\sqrt {{{(k - m{\Omega ^2})}^2} + {r^2}{\Omega ^2}} }}\\
\\
k = stiffness\\
m = mass\\
\Omega = frequency\\
r = damper\\
P = force
\end{array}
So, an increase in the angular...
Does changing the angular frequency change the amplitude of a forced oscillation? If so, I don't understand how that can be. I guess that the angular frequency is based only on the springs and dampers? So assuming those are the same then the angular frequency will always be the same?
Are...
I have worked out that this is a strongly dampered equation, so I expect the amplitude to die down quickly.
So, without frequency, this cannot be done? The question I have is to get the amplitude in order to solve the frequency between certain amplitudes. That last part can be done on the...
Hello,
I have worked out some force diagrams for forced oscillations and ended up with the solution as :
mx_double_dot+rx_dot+kx=Pcos(Ωt)
I am now asked to work out the amplitude. I know all of the variables except frequency(Ω). What equations can I use to find that?
Thanks.
Hello,
If I have a vector A and then I do the dot product on itself so A°A. Then can I use that to find the maximum distance from the origin? If I take the derivative of the dot product then can I know at what time the maximum distance was travelled?
I have done this but it is wrong...
I have the following simultaneous equations. However I am unsure how to handle that 2xy. Can someone give a pointer to any known methods?
x= 3x^2+2xy
y=x^2+3y+8
Hello,
I have three differential equations, for these I have found the eigenvalues and eigenvectors. After that I made a vector general solution for the system of equations. From this vector, how can I predict the long term behaviour of the system?
-Thanks.
Hello,
I am having some problem with some algebra:
1 -x(t)= −Bω2 cos(ωt) −Cω2 sin(ωt)
2 - x(t)=−ω2 x(t)
Can someone explain how we went from 1 to 2?
Thanks.
OK, I think that just got me the equation for the acceleration of a resisted projectile
r(t)= -g - (c*D^2*v/m)
So, differentiating this twice should give the acceleration componet? I know the answer I should get and it does not match. Any help?
Homework Statement
A ball travels vertically upward with quadratic air resistance, find the acceleration component.
Homework Equations
So, I have x pointing vertically downward and
C=0.20 D = Diameter V=velocity
W= -mgi
R = -C^2D^2V^2
F=ma
ma= -mg-C^2D^2V^2
The...