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| These answers are provided for you to check your work. If you get one of these answers and it does not follow from your work the graders have been told to give you a ZERO for the problem. The answers provided are not guarenteed to be correct. If you get a different answer be sure to talk to your professor and email bradley.burchett@rose-hulman.edu with any corrections. In the answers provided sometimes only the magnitude is given and not the direction. For your homework be sure to include the magnitude and direction when appropriate. |
| HW 01 |
||
| problem | hint | answer |
| 1.4 |
none provided |
none |
| 1.7 | To
determine whether the beam spring is in series or parallel
with the ideal spring, you need to figure out whether the
springs have the same force (series) or same displacement
(parallel). |
keq
= 1098 lbf/in meq = 0.031 slugs |
| top |
||
| Problem Set P-02 | ||
| problem | hint | answer |
| P2.2 | Draw FBD=KD and take moments about the point of contact. Use kinematics to link x and theta, then make substitutions to eliminate theta. Note that the spring force and damper force are already in terms of x. | |
| P2.4 |
The motion of the platform on the right is the
input to the system. This is a displacement input, not a
force input. Make sure to correctly specify the relative
displacements of all springs and damper. |
hint |
| 2.12 |
Make sure to correctly specify the relative
displacements of all springs and dampers, that is,
the motion/displacement of one end relative to the other
end. |
hint |
| 2.21 |
See hint link to the right. |
hint |
| 2.11 |
The answer is a single EOM for the
system. See hint link. |
hint |
| Problem Set P-03 | ||
| problem | hint | answer |
| P5.1 | The highest derivative term in each eqn is the output of a sum block. | |
| P5.2 | No Hint. | b=3/2 k2=3 |
| P6.1 | Y(s) has two 'poles' at s=0. Be sure to include all the appropriate terms in the PFE. | |
| P6.2 | The second order term is underdamped, include both sin and cos terms. | |
| P7.1 | No hint. | ans |
| Problem Set P-04 | ||
| problem | hint | answer |
| P9.1 | Use Big Gun. Do NOT write a node equation at the op amp output. | |
| 3.23 | In part c, set omegac=5 and match coefficients with the TF. You will have 3 eqns. for 4 unks., so choose one element arbitrarily (say R) and solve for the others. You may use exact vaules. See problem statement for simulink settings, In simulink, use the search engine to find unfamiliar blocks. | |
| 3.17 | no hint | |
| 3.22 | Easiest to use 'BIG GUN' and let Maple do the algebra. Set the simulation end time to 2 ms (0.002). | |
| Problem Set P-05 | ||
| problem | hint | answer |
| 6.2 | No hint. | b) h=9.713 W/(m2-K) c)Bi=0.043 |
| 6.5 | The answer to part (a) assumed that the heat transfer only occurs out the top of the chip. Part (d): Recall the known response of a first-order system to a step input. | |
| P13.1 | No hint. | |
| TOP | ||
| Problem Set P-06 | ||
| problem | hint | answer |
| S-2 | no hint | |
| 5.2 | no hint | |
| 5.10 | Write dV=A dh where A is the area of the top surface of the water. | |
| 5.18 | No hint. | |
| 5.19 | No hint. | |
| Problem Set P-07 | ||
| problem | hint | answer |
| 3.20 | no hint | |
| 19.1 | Measure the amplitudes and set the Mag. Factor equal to the Amplitudes ratio. Find the phase shift and express as an angle to find time constant. For the second order system, notice that you are given the undamped frequency. |
a)K=0.925, tau=0.779 b)K=0.514, zeta=0.649 |
| 10.13 | For small angles x, sin(x) = x and cos(x) = 1 (approximately). | thetass(t)=0.202cos(3t - 0.068) |
| 10.11 | Use superposition. | |
| 10.12 | You did the modeling of this circuit in Problem P9.1--see your previous HW and hints above. | |
| Problem Set P-08 | ||
| problem | hint | answer |
| 24.1 | Poles and zeros are all second order. Ignore the damping ratio and plot the straight line approximation. | |
| 24.2 | Don't forget the gain. (Be careful). From the straight line approximation you should be able to determine the break points. | |
| 7.16 | no hint | |
| 26.2 | no hint | |
| 27.1 | Note the feedback TF. | |
| 27.2 | Use PFE / inverse LaPlace to find the CL step response. | |