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) /...
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...
Homework Statement
What are the region of validity of the following?
1/[z2(z3+2)] = 1/z3 - 1/(6z) +4/z10
Homework EquationsThe 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
I...
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...
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...
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!
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...
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...