F\left[ \frac{\partial f}{\partial x} \right] = ikF[f]
http://www.thefouriertransform.com/transform/properties.php#derivative
where 2*f*pi = k
Looking over some properties, I can't seem to find what this would transform to. I think we can agree that x needs to go on the RHS and y...
Homework Statement
Use Fourier transform to find the solution of the following differential equation:
\frac{\mathrm{d^3}y }{\mathrm{d} x^3}+ \lambda \frac{\mathrm{dy} }{\mathrm{d} x} - xy = 0, \lim_{x \to \infty } y(x)=0
Find the asymptotic of the solution for lambda>> 1. Normalize the...
I used 1/3 because the conversion from angular to tangential is a/r or v/r.. and the ball is 3a away.
The equation should have the input force in it though.
Ok, well I see that angular acceleration is equal to tangental accel/radius
and angular velocity is equal to tangental velocity / radius
and angular position is equal to tangental position / radius
so...
(1/3)m\ddot{x}=-(1/3)\dot{x}-kx
on to something?
Are you talking about finding the actual distance x the ball drops down once the 5N force is applied?
I would think you take a moment at point O to find the force of the spring the instant after the system is released.. which would give you
\sum Mo=0 ; 5N(3a)+(kx)(a)=0
kx= (5N*3a)/(a) =...
Homework Statement
Assume a rigid body with a massless rod that pivots about point O. Displacement x is measured from equilibrium position. Assuming x is small, that the weight at the end of the rod is 5N and spring constant is 400n/m, obtain the dynamical equation of the system...
(I made a mistake with the 1/10 term, should be +)
anywaysOK! I think I figured it out..You can sub the integral parts for a variable.. in this case i'll call it Y
So I solve for Y, plug it back in where the integral was.
for y I ended up with
Y = (100/101)(20et/10 - et/10cos(t) +...
So I redid my integration and got..
et/10x = 20et/10 - et/10cos(t) - (1/10)et/10sin(t) - (1/100) \intet/10sin(t)dt
cmon brain don't fail me now.. i still don't see it arg
I'm all for the easy way (dont shoot me!) but what I don't see in your way is why you only multiplied one side by the integrating factor. Should you multiply the other side as well?
As of right now I'm still stumped.. but I did realize I made a mistake with a sign.
After integrating twice I end with:et/10x = 20et/10 + 10et/10sin(t) - 100et/10cos(t) - 100 \intet/10sin(t)dt I think I might see something..
\intet/10sin(t)dt = et/10x-20et/10?Still a noob with the symbols...
I think its coming back to me.. I need to find an integrating factor
I found that the integrating factor would be e-.1t
If I multiply both sides by it and integrate I end up with:
e-.1tx = -20e-.1t+int(sin(t)e-.1tdt)
So I end up having the int(sin(t)e-.1tdt)
Which isn't being...
I messed up on the title of the thread.. I had a few questions but ended up solving them on my own. The only question I have is how to solve this ODE. Thanks.
Homework Statement
Solve the ODE
(dx/dt)= f(t) - .1x
Where f(t) = 2+sin(t)2. The attempt at a solution
I faintly remember doing...