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Reading: all of Chapter 8, Chapter 9, sections 2, 3 and 5.

Exercises: 8.15, 8.16, 9.4, 9.7 and 9.8. Use the matlab step() command for 9.4.

On problem 8.16 part four, it asks for the transfer function from the input torque to the angular velocity. I don't have a angular velocity term in my equations for that part. Is it possible to go from the angular position transfer function to the angular velocity transfer function, or have I set up my equations wrong?

Yes it's possible to go from position to velocity. Just think of what differentiation is in the frequency domain.

For the same problem, how would we differentiate the transfer function?
Would it be d(theta/tau)/ds = d(...)/ds, or would it be
d(theta)/ds =d(tau*...)/ds

jgalezie wrote:For the same problem, how would we differentiate the transfer function?
Would it be d(theta/tau)/ds = d(...)/ds, or would it be
d(theta)/ds =d(tau*...)/ds

It's waaaaaaaaaaay easier than that. It is basically less than a one-line problem. You have to think about derivatives and Laplace Transsorms.

Since the inductor in part 2 of 8.15 is a coil of wire much like the coil in part 1, do we need to account for it's effect on the mass (i.e. a force) in addition to the velocity-affecting circle in the high-pass filter? Or can we ignore its effects to simplify the transfer function?

In the first part the inductance wasn't needed because the transfer function was from X(s) to I(s). However, in the second part you must consider the inductance because the input is the voltage, and the current though the speaker coil will depend on the voltage, inductance and the other circuit parameters.

for problem 815 I can't see to find an equation that gets it in terms of vin and x only so that I can solve for the transfer function. I cab only come up with 5 equations, one for the sum of the currents, the current through the capacitor, two for the the voltage in, and then 1 for the motion. However i seem to have 6 varying functions in them

Since the inductor in part 2 of 8.15 is a coil of wire much like the coil in part 1, do we need to account for it's effect on the mass (i.e. a force) in addition to the velocity-affecting circle in the high-pass filter? Or can we ignore its effects to simplify the transfer function?

Jessie wrote:for problem 815 I can't see to find an equation that gets it in terms of vin and x only so that I can solve for the transfer function. I cab only come up with 5 equations, one for the sum of the currents, the current through the capacitor, two for the the voltage in, and then 1 for the motion. However i seem to have 6 varying functions in them

That would be exactly the number you need to find the transfer function. One way to think of it is to use 4 of the equations to eliminate 4 variables, leaving one equation with two, and that remaining equation can give the transfer function. I would use KVL twice for two of the loops, KCL once, Newton's law once and equation 8.26.

mmarszow wrote:Since the inductor in part 2 of 8.15 is a coil of wire much like the coil in part 1, do we need to account for it's effect on the mass (i.e. a force) in addition to the velocity-affecting circle in the high-pass filter? Or can we ignore its effects to simplify the transfer function?

The magnitude of the force on the mass is given by equation 8.26, and you don't need to consider any other sources of force. The effect of the moving mass on the circuit is given by the velocity-affected circle. The rest is given by Kirchhoff's laws and Newton's law.