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Homework Statement Hello! I've been really unsure of whether my solutions to the first problem and part (b) of the second are right. My book gives few examples and so I've been trying to look on other websites for resources. Sorry if this is a lot, but any and all help would be appreciated...

Homework Statement Homework Equations Kirchoff's Voltage/Current Law The Attempt at a Solution I first started by summing up the currents at node 1, which is the intersection of 3 wires at the top, and node 2, which is between the capacitor and inductor. So, at node 1: $$ \sum i = -i(t) +...

So if I say k(x_1) = 5k(x_2 - x_1) + k(x_3-x_1). Is it right to say that x_1 = (5x_2 + x_3) / 7? Or should I express it some other way?

Thank you so much! But one more thing: I was taught that the force due to a spring is given by k(x_near - x_far), where x_near is the node whose restoring force is being considered. Could you clarify that concept for me a bit more in terms of this problem? I would very much appreciate it. Take...

Ah. This makes everything so much more clear. So then the forces of the three springs to the right of node 1 are opposite in direction to the force of the spring to the left. The parallel springs connected to node 2 have a k_eq of 2k = 3k = 5k. The tension in this spring is equal to then...

I'm having a hard trouble understanding. Could you help me please draw a FBD for node 1? I thought that the force went through the nodes, so that the force balance is just k(x_1) = x(t). Thank you so much.

Thank you for the reply. Are my FBDs right though? So assuming that they are: For node 1: k(x_1) = x(t) For node 2: 6k(x_2 – x_1) = x(t) For node 3: 30k/11(x_3 – x_1) = x(t) Is this the system of linear equations I am looking for?

Homework Statement Homework Equations f_spring = k(x_near - x_far) The Attempt at a Solution a. FBD: The force goes through the nodes, and the sum of the forces must be 0 because the nodes are massless. Therefore, kx_1 = x(t) So x_1(t) = x(t)/k b. FBD: For this system, the parallel...

Homework Statement Homework EquationsThe Attempt at a Solution I'd like to see if I have the right line of thinking in my solutions: a. The sampling frequency should be such that no aliasing or folding occurs, so it should be twice the frequency of the original signal. $$x(t) = -17...

Thanks. For Gauss's Law, I am using a Gaussian sphere to encompass the sphere. I do know for a fact that the electric field outside of the sphere is the same as a point charge - I guess I used Gauss's law because I thought the problem was testing my knowledge of finding E-fields and using that...

Homework Statement a. Calculate the energy density of the electric field at a distance r from an electron (presumed to be a particle) at rest. b. Assume now that the electron is not a point but a sphere of radius R over whose surface the electron charge is uniformly distributed. Determine the...

Thanks! But are part b and c correct? That is for part b, I would just need to differentiate part a with respect to y, and then part c the electric field perpendicular should be 0.

Thank you so much for helping me. I am understanding this concept a lot more now. I just have a few more things: I get the difference between r and y now. So then, if I say z is the distance between point P and some element dQ, then I also define dQ = lambda*dz dV = dQ(4*pi*E_0*r) =...

Sorry, what I meant was, I need to find V using dV = dQ/(4*pi*E_0*r). In this case, r is y, and dQ is lambda*dL, that is, dQ is the charge of a really small length along the rod dL. So then, can I set the bottom of the rod to be 0, and integrate from 0 to L? Why can't I integrate from y to y+L...

Ah. So I would need to find a dQ value over 1/(4*pi*E_0*y) to integrate? So, since Q = lambda*L, dQ = lambda*dL? And then the integral would go from y to y+L?