|
|
|
|
|
|||
 |
 |
 |
 |
 |
 |
|
|
|
||||||
| 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. |
| Problem Set P-01 | ||
| problem | hint | answer |
| 1.4 | no hint | |
| 1.7 | Note that the spring deflection equals that of the beam midpoint. | meq=0.031
sl keq=1098 lb/in |
| Problem Set P-02 | ||
| problem | hint | answer |
| P2.1 | Use tables and be careful with units | L=12.0in |
| P2.2 | Take moments about the point of contact. Use kinematics to covert theta_dot_dot to x_dot_dot. | |
| P2.4 | Note spring and damper forces are proportional to relative displacement and relative velocity respectively. | |
| 2.12 | Note spring and damper forces are proportional to relative displacement and relative velocity respectively. Note carefully how each spring and damper is anchored. You might want to do Text 2.8 before attempting this one (see below). | |
| 2.21 | Write the EOM of the load mass using gear 2 angle as the input. Use kinematics to sub the actual input in place of gear 2 angle. | .pdf |
| 2.6 | Use gear kinematics to write theta_2 in terms of theta_3. Spring k2 deflection can be initially written in terms of theta_2, subbing in theta_3 later. | .pdf |
| 2.11 | Note this is a single degree of freedom system--you can write theta_2 and theta_3 in terms of theta_1. Note that gear one is rigidly attached to the small mass. Gear 2 is rigidly attached to the large mass. Thus you should draw 3 FBDs, 1. Gear 1 and small mass, 2. Gear 2 and large mass, 3. Gear 3. Solve for gear tooth forces in terms of theta_1 and theta_2 respectively. Sub the tooth forces into your theta_1 equation, then use kinematics to write all in terms of theta_1 and its derivatives. | .pdf |
| Problem Set P-03 | ||
| problem | hint | answer |
| P5.1 | Each first derivative is the input to an integrator. Set the (step) inputs to zero for free response. | .pdf |
| P5.2 | You need FBDs of each mass and an FBD of the lever. Keep in mind that spring forces are proportional to relative displacement. From the lever FBD write a moment equation about the pin joint and solve for the unknown link force in terms of all other params. Subs this expression into your mass 2 equation. Use the lever kinematics to write x3 in terms of x2 only. | .pdf |
| 3.25 | Write KCL for the node containing the solid and hollow circles. Write element laws for all elements and subs into KCL. | See p. 171 of the text. |
| P6.2 | Write KCL for the nodes at the top of R1 and R2. Write element laws for all elements and subs into your KCL equations. Use Maple to solve for the TFs. | .pdf |
| P7.1 | Use BIG GUN. Use Maple to solve for the TF. | .pdf |
| P7.2 | Write KCL for the node defined by the negative op amp terminal. Note that the positive terminal voltage is not zero--it is equal to the node voltage between R2 and R3. | .pdf |
| 3.17 | Choose coordinates theta1 and theta2 for the massless gears. Also define a coordinate thetan for the node between damper c2 and spring k. Replace theta2 using the gear kinematics. | |
| 3.22 | Easiest to use 'BIG GUN' and let Maple do the algebra. Set the simulation end time to 2 ms (0.002). | .pdf |
| TOP | ||
| Problem Set P-04 | ||
| problem | hint | answer |
| 3.20 | Get the op amp and motor loop equations in first order form in terms of dei/dt. Next solve the g state definition for eA and differentiate to get deA/dt in terms of dg/dt. Equate this expression with your deA/dt equation and solve for dg/dt. Substitute for eA in terms of g in the diA/dt equation. | .pdf |
| P7.1 | Combine all impedances into one and use I1(s)/V1(s)=1/Ztot. | .pdf |
| P12.2 | Find the system transfer function then refer to Section 3.4.1 for handling sn terms in the numerator. | .pdf |
| P13.1 | No hint | .pdf |
| TOP |
||
| Problem Set P-05 | ||
| problem | hint | answer |
| P14.1 | Apply quadratic formula to (m+M)s2+cs+k=0 to get pole locations. For each damper, plot the pole locations using k = linspace(0.09,2.09,10)*1000. Answer posted uses >>axis([-10 10 -10 10]), >>axis equal to zoom in on design space. | .pdf |
| 4.10 | Use 'trig function' block in 'Math Operations' to handle the sin term in Simulink. c)Find the PFE and theta(t) for theta(0)=1. You can then scale the linear response by the actual theta(0). | .pdf |
| TOP | ||
| Problem Set P-06 | ||
| problem | hint | answer |
| 5.2 | Note that you must use absolute pressures since you are multiplying and dividing to get current pressure. Write expressions for the total volume, and water volume as a function of h, then subtract to get the current gas volume. Your final answer may be a list of four equations 1. dh/dt, 2. Initial gas volume, 3. Current gas volume, 4. and P = P0VG0/VG | .pdf |
| 5.10 | Draw a side view and use similar triangles to get the length of the top edge of the water as a function of height. Next draw a top view and use similar triangles to get the depth (into the page) of top water surface in terms of h. Now use dV=Adh to get dV/dt for COM eqn LHS. | .pdf |
| 6.2 | Top half of grape radiates to the sky, bottom half receives radiation from the ground. | 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. | |
| TOP |
||
| Problem Set P-07 | ||
| problem | hint | answer |
| P20.1 | All eqns required for this problem can be found on text p. 187. | |
| 10.13 | No hint | |
| 10.11 | Use TF method and superposition. | |
| 10.12 | Use BIG GUN to get the TF. | |
| P24.1 | No hint | |
| 10.10 | Part a: the denominator factors into first order terms. | |
| Problem Set P-08 | ||
| problem | hint | answer |
| P25.1 | Numerator and denominator have second order terms--use square root of the s0 coefficient for break frequency. | No answer. |
| P25.2 | Extrapolate the low frequency part of magnitude curve to get Bode Gain. Be careful simplifying! | |
| P26.1 | Denominator has one real and two complex poles. Might be helpful to draw the individual terms to see how the first order pole at -2 combines with the second order zeros at -2. | |
| P26.2 | TF has an origin zero and a pole/zero cancellation at s=-5. Denominator factors into three real poles. | |
| P27.1 | Use Figure 11.1 and Eqn 11.3 from the text. | |
| P27.2 | H(s)=1 in Eqn 11.3 from the text. Use the partial fraction expansion to get analytic step response. | |
| TOP | ||