2Solution Page 14.929.5To find the damped natural frequencies of the system one sets: ms 2 + (c1 + c 2 ) s + k1 + k 2 (c 2 l 2 − c1l1 ) s + k 2 l 2 − k1l1 det 2 2 2 2 2 = 0. (c 2 l 2 − c1l1 ) s + k 2 l 2 − k1l1 Js + (l 2 c 2 + l1 c1 ) s + l 2 k 2 + l1 k1 With the aid of MATLAB and using given system’s parameters, one finds the followingdamped natural frequencies with their corresponding damping ratio and naturalfrequencies. ωd 1 = 4.9676rad / s
3 3 -S U MAc ? 0 : / MAc / Ä L - 2 L Õ © PL ? 0 MAc ? / 5PL MAc ? 5PL S Å 3 Ö 2 EI 6 EI 6 EIBy rules 9 and 10 in Section II, the slope sA and the deflection yA at the free end A of the actual cbeam in Fig. 3 are, respectively, given by the “shearing force” VA and the “bending moment” cM A at the fixed end A of the conjugate beam in Fig. 4. We write PL2 3 sA ? VA c ? Acy ? yA ? MAc ? / 5PL 2 EI
regular use of taxonomic language throughout thefull duration of the statics course will help with long-term retention of conceptual understandingto support procedural approaches to problems.The objective of the current work-in-progress is to present the early stages of development of theTOPS to a community of educators and researchers that can provide valuable feedback prior tothe tool being applied in the first phase of the aforementioned research design.References[1] R. Streveler, T. Litzinger, R. L. Miller, and P. S. Steif, “Learning conceptual knowledge in the engineering sciences: Overview and future research directions,” J. Eng. Educ., vol. 97, no. 3, pp. 279–294, 2008.[2] M. T. H. Chi, “Three types of conceptual change
S, D Q, S, D S, Q, D5.2 Find items under bending5.3 Bending members with commoncross-sections5.4 Feel craft sticks bending5.5 Stress Opticon: Bending stressdistribution S, Q, D5.6 Quantify flexure in a craft stick5.7 Stress Opticon: simple support5.8 Photoelastic beam bending S, D S, Q, DStress Transformation7.1 Directional Strength (Craft Stick) S7.2 Directional Orientation inStructures7.3 Photoelasticity: Beam with holes S, Q, D7.4 Matching loads and failure planes7.5 Brittle and Ductile Failure
presenting the total externalwork and total strain energy equations beginning first with a single load P applied to a planartruss with one load sequence. Then loads P and Q are applied using two load sequences in whichthe load Q is applied at the location and in the direction of the desired displacement. From thisbasis of understanding, an additional load S is included in both load sequences to discuss itsinfluence on the displacement expression. This leads to a general understanding of the influencethat any number of additional loads would have on the displacement expression, and that theeffect of the load Q remains unchanged as these loads are applied. It then becomes evident thatBarry T. Rossonthe desired displacement due to all the applied loads
cos m/s, 0 s ≤ t ≤ 5π s. 5 (b) the distance STOP STOP between the two stop signs; and 20 (c) the acceleration at 15
) ℎ = 𝑐𝑐 sin 𝛿𝛿 Figure 6: The dimensions g and h can be related to r through the angle θ3. Figure 7: The dimensions g and h can be related to s through the angle 𝜃𝜃3 .Next, going back to the variables r and s defined earlier, we can write 𝑟𝑟 = 𝑔𝑔 cos 𝜃𝜃3 + ℎ sin 𝜃𝜃3 (25) 𝑠𝑠 = ℎ cos 𝜃𝜃3 − 𝑔𝑔 sin 𝜃𝜃3as shown in Figure 6 and Figure 7. We now have two equations with one unknown, θ3. Eachequation is transcendental and difficult to solve on its own. Therefore, we will employ a fewtricks to isolate θ3. First
24Substituting the above solutions into foregoing equations for EIy¦ and EIy , we write C1 8 w0 L3 8 w0 L3 sA ? y¦(0) ? ? sA ? S EI 3EI 3EI Page 12.1535.5 C2 131w0 L4 131w0 L4 yA ? y (0) ? ?/ yA ? fi EI 24 EI 24 EIIV. Analysis of a Hinge-Connected Beam: Wrong and Right WaysEmploying singularity
Cartesian coordinate system with the originat the initial position and upward as the positive 𝑦-direction.Example: The skier leaves the 20°surface at 10 m/s. Determine the distance 𝑑to the point where he lands [Example 13.7 in 3]. Table 1 Solution and Cognitive Load Analysis Solution Cognitive Load Analysis 𝑎𝑥 = 0, 𝑎𝑦 = −9.81 m/s2 Most students should be familiar with it so it will not be counted as a new item. 𝑣𝑥 = 10 ⋅ cos 20∘ m/s, No new item is introduced as most students should be able to figure
) presentingmore information to users through clickable pop-out boxes. The last three characteristics focuson students’ active involvement, giving them a chance to organize their learning process bynavigating through modules, changing input parameters, and observing the outcomes. Dependingon the technical limitations and CSA objectives, different researchers have focused on differentaspects of the above-mentioned characteristics 6, 11, 12, 17, 18, 24.Pedagogical innovations in the instruction of engineering mechanicsBefore 1990’s, the main emphasis of educational research was on improving teaching styles,active learning, and facilitation of student conceptual understanding20. Developments incomputer graphics and web-based tools have reinforced these
vector is BB¦ ? L tan fs ? L ÇÉfs - 13 (fs )3 - 152 (fs )5 - 315 17 (fs )7 - ©©©Ú L fs (3) fl¦¦ can be taken as equal as fs › 0 in theIn Fig. 2, the lengths of the chord BB¦ and the arc BBlimit. Equation (3) shows that the magnitude of the compatible virtual displacement of point Bmay indeed be computed by using the radian measure formula in calculus; i.e., s ? rs (4)where s is the arc subtending an angle s (in radians) included by two radii of length r
education. American Society for Engineering Education, Washington, 77.2. Lattuca, L. R., Bergom, I., & Knight, D. B. (2014). Professional development, departmental contexts, and use of instructional strategies. Journal of Engineering Education, 103(4), 549-572.3. Thomas, J. W. (2000). A review of research on project-based learning.4. Slough, S. W., & Milam, J. O. (2013). Theoretical framework for the design of STEM project-based learning. In STEM Project-Based Learning (pp. 15-27). SensePublishers, Rotterdam.5. Capraro, R. M., Capraro, M. M., & Morgan, J. R. (Eds.). (2013). STEM project-based learning: An integrated science, technology, engineering, and mathematics (STEM) approach. Springer Science & Business Media.6
⇤ ⇤ ⇤ ⇤ ⇤ Q3: The scenario presented in this problem seems realistic.Figure 6 shows the electrical modeling problem presented to the system dynamics class. For thisproblem, the context-rich version contained narrative placing the problem-solver in the role of astudent dealing with data being contaminated by 60 Hz line noise and also identified the circuitas a band stop filter.A) Consider the circuit shown in the figure below. L Vin C R Vout (a) Write a transfer function that relates the input voltage Vin to the output voltage Vout . (b) Of the three circuit components, which one(s) might be changed to alter the natural frequency of this circuit?B) Please answer the following
were focused on “day-to-day" work that is expected to be known by this point in theirschooling; others were extensions of basic theory, where the students were asked to implementtheir knowledge in more complex applications of their prerequisite work. Based on previous workwith engineering students solving word problems in mathematics, each of the problems on theMechanics test were presented as word problems with no figures provided. Examples of twolevels of difficulty used in the problems are provided in the following examples: • A 5kg otter needs to cross a 10m wide stream that is flowing at 10m/s. Assuming the otter can swim at a rate of 2m/s, how far up stream must she start to end up directly across from where she is
. Kinetics principle(s) and/or kinematics you Kinetics principle(s) and/or kinematics you would use: would use: 3. During a hammer thrower’s practice swings, the 4. Knowing that crank AB rotates about Point A 7.1-kg head A of the hammer revolves at a constant with a constant angular velocity of 900 rpm speed v in a horizontal circle as shown. If = 0.93 clockwise, determine the acceleration of the piston m and = 60, determine the tension in wire BC. P when = 30. Kinetics principle(s) and/or kinematics you would use: Kinetics principle(s) and/or kinematics you
. Another distinct advantagewith CAD visualization involves being able to modify the problem. As an example, whathappens to the tension in the cables if the angles of cables A and B are increased or decreased?Can you visualize that from the picture?Another basic problem which would not intimidate a CAD novice involves EngineeringDynamics to include the mysterious “acceleration” term which tends to bewilder students. Theproblem focuses on determining the total acceleration of a sliding collar on a straight rod rotatingabout a vertical axis when the rod’s current position is at 45° as shown in Figure 2 on the left. Atthis instant, the point P on the collar has a outward velocity along the rod of 4 m/s (relative to therod as shown) when the distance
So in a sense the question here is: Do students who exhibit specific difficulties in de-scribing rigid body motion at the beginning of Statics exhibit specific difficulties in assessingequilibrium at the beginning or end of Statics? If so, might identifying these students at the startof Statics allow the instructor(s) to more effectively address these students’ expected challengesand give those students a better chance of exiting Statics with a consistent and correct approachto assessing equilibrium? This work attempts to answer the first of these two questions.MethodologyTo test the notion that understanding a dynamic rigid body gives a better foundation for under-standing a static rigid body, students complete a pair of simple questions
/toolkit. Ourgroup and the various tasks each sub-group performs have been described in our past ASEEconference papers11-13.Some of the exercises we have developed and now assign to students every semester are listed inTable 1 below: TOPIC PROBLEM(S)Moment in 2D, Free-body Diagram SeesawEquilibrium of 1 rigid body or Frame Arm & PurseTruss: Method of Joint & Method of Section Minneapolis BridgeDistrib. Load, Centroid New Orleans Levee, Space StationFrame KeyboardCombined Frame & Truss BicycleFriction
representations listed in the two right columns include Pictorial, Symbolic, narrativeLanguage, Numeric, and Diagram. Item Relevant Vector Concepts Representations Question Answers 1 2D, position vectors, vector addition PL S 2 2D, cross product PLS L 3 2D, Cartesian components N D 4 2D, Cartesian components, vector addition DNS LN 5 3D, Cartesian components N D 6 3D
: Summative instructional events are now presented. Knowledge and learner centered. Go public: This is a high stakes motivating component introduced to motivate the student to do well. Learner and community centered.Challenge 2…NThe following progressively more ambitious challenges enable the student to increasinglydeepen their knowledge of the topic being explored. Repeat the complete legacy cycle for eachchallenge.Reflect BackThis gives student the opportunity for self-assessment. Learner centered.Leaving LegaciesThe student is asked to provide solutions and insights for learning to the next cohort of students,as well as to the instructor(s). Community centered. The legacy cycle contains steps or activities that appeal to
conversations withstudents, particularly with those who did very well in the initial assessment; it is plannedto implement this technique in a more formal manner in the next academic year alongwith well instrumented surveys to evaluate the success of DI in a undergraduatemechanics class.1. Tomlinson, C. & Kalbfleisch, L. (1998, November). Teach me, teach my brain: A call for differentiated classrooms. Educational Leadership, 52-55.2. Tomlinson, C.A., & Allan, S. D. (2000). Leadership for differentiating schools and classrooms. Alexandria, VA: ASCD.3. Fischman, B. (as viewed on Jan 17, 2007) http://www.education.pitt.edu/leaders/FAQ/differentiatedinstruc.htm4. Felder, R. M. (as viewed on Mar 7, 2007) http://www.ncsu.edu
tensormathematics, this approach prepares students for more advanced elasticity formulations andcomputational approaches to both solid and fluid mechanics. Page 26.1394.9 Skill #1 Formulate and solve beam deflection problems (outcome 3e). Superior 5 Identifies, explains and solves the equilibrium equation(s) and boundary conditions to determine the requisite deflection(s). Dimensions are consistent and correct. Good 4 Identifies (without explaining) and solves the equilibrium equation(s) and boundary
1983.9. Dollár, A. and Steif, P.S., “Learning Modules for the Statics Classroom,” 2003 ASEE Annual Conference and Exposition.10. Steif, P.S. and Dollár, A., “A New Approach to Teaching and Learning Statics,” 2003 ASEE Annual Conference and Exposition.11. Crouch, C.H., Fagen, A.P., Callan, J.P., and Mazur, E., “Classroom demonstrations: Learning tools or entertainment?” American Journal of Physics, June 2004.12. Yoder, D.C., Parsons, R., Pionke, C.D., and Weber, F., “Hands-On Teaching of Engineering Fundamentals,” 1998 ASEE Annual Conference and Exposition.13. 80/50 Inc., 1701 S. 400 East, Columbia City, IN 46725, www.8020.net. Page 12.151.12
science education literature onrepresentational competence discussed above, is to provide students physical representations ofthe abstractions used to construct these problems so they can develop a better conceptualunderstanding of these systems rather than just memorizing problem solving procedures. Asimplemented and described further below, the SMK activities generally provide the first exampleapplication(s) of the relevant concept(s) after students encounter new topics through pre-classreading assignments. Students can directly relate these models to the problems they see inexamples in the reading and homework assignments.The SMK approach offers several other benefits that can facilitate the inclusion of physicalmodeling activities in any
provided f1 is much greater than f2. CCW couple moment since the structure wants rotate CW. (correct answer choice) 2 students attempted It's stated that F1's magnitude is much greater than F2 so we can disregard to apply a heuristic the effect of F2 and focus on F1. A reaction at A would be equal and opposite (0 correct answers) of F1. It's my understanding that a single force cannot have a couple moment so it wouldn't have a couple but I'm still unsure on certain applications of couples. (incorrect answer choice) The point at A has a pin through it which does not
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questionwhether or not the module content best represents the BOK.As this step is the most practical part of the methodology to develop a curriculum, manyquestions about the details of teaching a course like this arise. Some of the modules may not bein accord with the traditional way the topics within the module have been taught. Thus, there arequestions about which examples to use, which textbooks or supplemental material should beused, and which professor(s) will teach the modules. Questions may also arise when combiningtopics in a module that have been taught individually either in a lecture or laboratory setting.This step requires time, patience and communication with those responsible for teaching thematerial and making the semester schedule
area (Q) can be obtained using the following equation: b(h 2 / 4 / y 2 )Q? (25) 2Determination of the Principal Stresses:A square differential element of beam subjected to the normal stresses sx and sy and a shearingstress txy is shown in Figure 4. To develop the expression for the principal normal and shearingstresses acting on the element of the beam, the equation for the normal stress s and shearingstress t on an inclined plane with an angle of inclination of s are obtained first. uy A v xy ux
type of course content can be intensive. Our hope is that by presentingsome of our own work, methods, and tips, other Statics instructors are able to pave their ownpath towards contextualizing Statics in their own classrooms. While interested readers areencouraged to adopt the examples and projects we have presented here as a starting point, wehope our work will inspire others to develop their own context examples to, in turn, inspire theirown students to see Statics everywhere in the world around us.References[1] S. Moseley, “One Paragraph and a Few Simple Questions - Giving Statics Problems Human Context,” in ASEE Annual Conference and Exposition, Conference Proceedings, 2017, p. 6.[2] G. L. Downey, “PDS: Engineering as Problem
13.1382.6SDOF system are shown in -1Figure 4. From the swept sine -1.5 -2 0 10 20 30 40 50 60 70 80 Time (s) Figure 4. Typical time response for a swept sin inputresults the FRF can be calculated in Matlabusing the built-in command called“tfestimate.” A typical FRF generated thisway is shown in Figure 5.This lab was also used to begin