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    Engineering Circuit Analysis (Equation) with Multiple Voltage Sources

    Homework Statement Derive the differential equation that relates the voltage (V) to the current (I) entering the circuit. Homework Equations Let: ic = C dV/dt = current traveling through the capacitor (C) ik = (V+Ek) / Rk = current traveling through the potassium (K) channel iNa = (V-ENa)...
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    Transfer Function of Block Diagram

    Homework Statement The block diagram of a PM DC servo motor with current loop feedback is shown below: If Ki is adjusted such that J(Ki+R)2 >> 4KTKbL, show that the transfer function may be approximated by G(s) = (1/Kb) / (τms+1)(τes+1), where τm = J(R+Ki) / KTKb τe = L / (R+Ki) The...
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    Singularities of a Complex Function

    Homework Statement What are the region of validity of the following? 1/[z2(z3+2)] = 1/z3 - 1/(6z) +4/z10 Homework Equations The Attempt at a Solution Knowing that this is the expansion around z=0, I am trying to find the singularities of the complex function. Which is when z2(z3+2) = 0...
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    FBD of Flexible and Rigid Body Coupling

    Thank you Dr.D, that makes sense now!
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    FBD of Flexible and Rigid Body Coupling

    Problem: I am having a bit of problem with the signs on the force balance with the constraining force. The system is: Attempt: I drew the FBD with the constraining force for the lumped mass: Then I tried to solve for the constraint force in terms of the spring and damper: For the...
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    Vibrations - Rayleigh-Ritz Method Admissible Functions

    Great! Thank you so much! If I may ask one more slightly related question: If I am using the Assumed Modes method for N=4, for the stiffness and mass coefficients, do the i and j just need to add up to 4? For example, I could use: mij = m1,3 or mij = m2,2 I'm not sure if that question is...
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    Vibrations - Rayleigh-Ritz Method Admissible Functions

    Thank you for the quick response Dr. D! So in that case, could I choose a function (like before): φi(x) = 1 - cos(2πix/L), i = 1,2,3,... φj(x) = 1 - cos(2πjx/L), j = 1,2,3,... Where they would end up being φ1(x) = 1 - cos(2πx/L) φ2(x) = 1 - cos(4πx/L) φ3(x) = 1 - cos(6πx/L)... Thank you!
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    Vibrations - Rayleigh-Ritz Method Admissible Functions

    Hi everyone, I'm having a bit of difficulty choosing an admissible function for a fixed-fixed nonuniform bar. I chose the function φ(x) = 1 - cos(2πx/L). But when solving for the the stiffness and mass coefficients: kij = ∫EA(x)φiφjdx mij = ∫ρ(x)φiφjdx, I am not sure where I should have...
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    Equation of Motion of Mass Damper and Rotating Bar

    Homework Statement Consider the inverted pendulum system, where a uniform rigid bar of mass m and length L is elastically hinged on top of a lumped mass M. The bar is constrained by a torsional spring of coefficient kτ and the mass is constrained by a damper of coefficient c. Derive the...