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    Green's function for a critically damped oscillator

    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?
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    Green's function for a critically damped oscillator

    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}...
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    Green's function for a critically damped oscillator

    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...
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    Green's function for a critically damped oscillator

    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) =0 Homework Equations x(t) = ∫ dt' G(t,t')F(t') from 0 to T The...
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    Calculating the ripple factor from oscilloscope

    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?
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    Calculating the ripple factor from oscilloscope

    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...
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    Classical mechanics equation of motion

    thanks once again :D
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    Classical mechanics equation of motion

    hahah yes! omg how could I not see that!
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    Classical mechanics equation of motion

    Hey wait! integration of 0 to 0 for any function is 0 right? so v_0 = C :O
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    Classical mechanics equation of motion

    mmm.. \dot z(0) = {1 \over m} \int_0^0 e^{γT} F(T) dT + C I really have no clue on this part :S
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    Classical mechanics equation of motion

    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 :(
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    Classical mechanics equation of motion

    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...
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    Classical mechanics with time dependent force

    Hehe I got that! Thanks for the reminder and help! :)
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    Classical mechanics with time dependent force

    oh i see i see. for the r(t) equation do you mean the initial conditions?
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    Classical mechanics with time dependent force

    I got the equation :) thanks! however just a quick query, why is there a need for the different symbols when integrating if it's the same closed intervals?
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    Classical mechanics with time dependent force

    v(t) = v_0 + 1/m ∫F(t) dt from 0 to T r(t) = v_0T + 1/m ∫∫ F(t) dtdt from 0 to T But it makes not much sense from this equation because there is a last part that says check that you get the familiar results when F(t) = mg is constant in time
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    Classical mechanics with time dependent force

    Hi both! thanks for the replies. iloveserena: I was trying to simplify things by considering the z-direction forces first, maybe i was over-simplifying/ Now assuming I follow stallionx's equation, then v(t) = v_0 + 1/m \intF(t) dt from 0 to T v(t) = v_0 + \intdv/dt dt from 0 to T v(t)...
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    Classical mechanics with time dependent force

    Homework Statement A point mass m is exposed to a time dependent force F(t). Determine the position r(t) of the point mass for the initial conditions r(0) = r_{0}and v(0) = v_{0} Homework Equations The Attempt at a Solution \sumF= ma F_{z}(t) - mg = ma a = 1/m F_{z}(t) - g...
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    Coordinate systems

    ohh!! I got it!! omg lol thanks alot!
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    Coordinate systems

    Hmmmmm okay I can see how that would give me the correct answer.. But still I am a little confused about this formula on wiki because in my text book, the gradient in cylindrical coordinates formula is as the one I stated above. In particular, vs just {\partial \left( A_s \right) \over...
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    Coordinate systems

    Ops, I meant the cross of r. (edited that, thanks for pointing out) I'm pretty sure the gradient formula is correct as checked on the wiki link you gave. Do you mean my r vector is wrong? \vec{r} = s\vec{s} + z\vec{z} Well I looked through my workings and I'm quite sure I got that right as...
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    Coordinate systems

    Homework Statement For the cartesian, cylindrical, spherical coordinate system, prove that \nabla.\vec{r} = 3 and \nablax\vec{r}=0 Homework Equations For cylindrical coord system, \vec{r} = s\vec{s} + z\vec{z} \nabla = \vec{s} \delta/\deltas +...
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    Physical pendulum

    Homework Statement http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html#c2 i'm trying to prove to be Homework Equations Letting d = Lcm now we already know \partial^2\vartheta/\partial t^2 = \alpha = mgdT\vartheta / I I tried integrating the whole equation wrt dt so...
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    Calculating acceleration due to gravity question

    mass can be considered irrelevant. yes it is negative because acceleration is a vector and we took upwards as positive in our kinematics equation (i.e. positive 11m)
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    Calculating acceleration due to gravity question

    you have initial velocity, final velocity and displacement
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    Momentum conservation

    correct. momentum is not conserved. in this case, since the wall is hinged to the ground/celling, a reaction force from this places is acting against the force that tries to move the wall.
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    Massless pulley and acceleration

    The more mass an object has, the slower the acceleration when subjected to the same force. No doubt the pulley will experience infinite acceleration, but do not simply equate this to be the same as m1's acceleration. There are many other factors to consider such as how the pulley is attached...
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    Massless pulley and acceleration

    No. Tension is a force, do not confuse it with resultant force! In a way, it is true that the acceleration of the string is infinity as well. You should be considering either of the mass blocks as a FBD
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    Massless pulley and acceleration

    correct me if im wrong but massless objects are an ill-defined concept to begin with. Considering F = ma a= F/0 or infinity in other words. I wouldn't say it's 0 acceleration.
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