Recent content by Safder Aree

Oh no you're right, $$ -(2 \pi w)^2 \hat{u_t} + 4 \pi i w \hat{u_t} = - \hat{u}(x,t)$$ Would that be right? Where would I go from here?

So my understanding is that then applying the transform leads to: $$ -(2 \pi w)^2 \hat{u_t} + 4 \pi i w \hat{u_t} = - fourier(constant)$$ Is the Fourier of a constant a dirac delta function?

I am struggling to figure out how to approach this problem. I've only solved a homogenous heat equation $$u_t = u_{xx}$$ using a Fourier transform, where I can take the Fourier transform of both sides then solve the general solution in Fourier terms then inverse transform. However, since this...

Then current is, $$I = VR_{total}$$ $$= V (R_s + \frac{1}{R_p} + \frac{1}{R_I})$$

Then for the case $R_p$ is introduced, it should be one half of that value right?

So I know that ##I_m## must be: $$ \frac{V}{R_s + R_I}$$? Not sure where to go from here.

I made a typo. R_parallel is actually $$ R_{parallel} = \frac{1}{R_p} + \frac{1}{R_I}$$ To get ##R_s## and ##R_p## I used the values from a variable resistance box. The ##R_s## value was found first in a circuit where there was no ##R_p##, the value was what gave the meter movement full scale...

Homework Statement Given this following circuit: What is the internal resistance of the meter movement ( R_I). This is part of a project I'm doing and I know the equation that gives you the internal resistance in this circuit. $$R_I = \frac{R_sR_p}{R_s - R_p}$$. However, I have no idea how...

I'm not sure if I am parametrizing this correctly, would you be able to double check where i am going wrong? So for the path 0 -> 1. $$z(t) = t, z'(t) = 1$$ $$\int_0^1 e^t dt $$Path 1-> 1+i $$ z(t) = 1 + it, z'(t) = 1$$ $$\int_0^1 e^{(1+it)}dt $$ Path 1+i -> i $$z(t) = 1+i -t, z'(t) = -1$$...

That makes sense. Thank you. I'll just solve the integral.

Homework Statement Show that $$\int_C e^zdz = 0$$ Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 +i and z = i. Homework Equations $$z = x + iy$$ The Attempt at a Solution I know that if a function is analytic/holomorphic on a domain and the contour lies...

I actually forgot to mention that we are to assume small oscillations. I'm still quite confused on where to proceed with this question. How would you go about averaging the vertical component. Would T: $$Tcos(\theta) = mg$$ $$Tsin(\theta) = F$$ Thus $$T = \frac{mg}{cos(\theta)}$$

Sorry, I'm not sure I follow.

Homework Statement Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much? Homework Equations $$F = -mgsin\theta $$ $$T = mgcos\theta $$ The Attempt at a Solution I'm mostly confused by what it means by time average. However from my...

I personally found working through Stewart's Calculus along side Spivak's Calculus to be the best. Stewart has tons of problems and you can find all the solutions online and Spivak provides a more comprehensive coverage of topics. Both of them have helped me do well in undergraduate degree.