Hmm nope I have never heard of the residue theorem. I tried wiki-ing it to see how it works, but it looks complicated. Is there any other way to do this?
im really bad at Fourier transform, so i didnt follow your advice..
but i did try considering the force being written as a Fourier transform
f(t) = 1/2\pi∫F(w)e^{iwt} dw
and the dirac delta
δ(t-t')= 1/2\pi∫ e^{iwt}e^{-iwt'} dw
so i went ahead to solve and i got that
G(t,t') = x_{h}...
Hello! thanks for you reply! :)
yeah you are right, i missed out the x there
not sure if i got it right but on the RHS, i got \frac{1}{2\pi}\frac{1}{i(t-t')}e^{i\omega(t-t')}+C
is this right?
oh and (d²/dt² + 2γd/dt + ω0²) G(t,t') = δ(t-t')
so i should be solving as usual 2nd order...
Homework Statement
Consider critically damped harmonic oscillator, driven by a force F(t)
Find the green's function G(t,t') such that x(t) = ∫ dt' G(t,t')F(t') from 0 to T solves the equation of motion with x(0) =0 and x(T) =0Homework Equations
x(t) = ∫ dt' G(t,t')F(t') from 0 to TThe Attempt...
Hi berkerman. Thanks for the reply. I could possibly go find a ripple diagram when i get back home.
For the Vac do you mean that you just take it as Vpp. Meaning the ripple factor is given by Vpp/Vavg?
Hello fellow physicists!
I have a lab about rectifying and filtering circuits and I was asked to calculated the ripple factor using an oscilloscope.
I managed to get the ripple waveform shown on the oscilloscope, but the thing is there are so many values to read off I have no idea which to...
Omg hi iloveserena again hahaha
For \dot{z}(t) = e^{-\gamma t}/m \int e^{\gamma t} F(t) dt
v_0 = 1/m \int e^{\gamma t} F(t) dt
This is the part I'm stuck at, I'm not sure what to do with the integration function :(
Homework Statement
A point mass m moving along the z axis experiences a time dependent force and a fricitional force. Solve the equation of motion
m\ddot{z} = -m\gamma\dot{z} + F(t)
to find v(t) = \dot{z}(t) for the initial velocity \dot{z}(0) = v_0
Hint: what is the time derivative of...