A mechanical system consists of a mass M, a damper B, two springs and an ideal...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A mechanical system consists of a mass M, a damper B, two springs and an ideal gearbox (i.e. negligible inertia and friction) as shown in Figure 1. An external force f(t) is exerted on the mass. For the gearbox, an input angular displacement of produces an output angular displacement of 0o =20. At rest with no external force applied, 0,0 = 0 rad. The input and output levers ('arms') connected rigidly to the input and output shafts of the gearbox, respectively, are both of unit length and have negligible mass. Both springs, one (with Hooke's constant K) connected to M and the other (with Hooke's constant K) connected to the output lever of the gearbox, are rigidly attached to the wall on the left. Both the wall and gearbox are inertially stationary. Assume the applied force to be always sufficiently small to ensure that the displacement 12 remains very small. Output & Input Levers K www ee Gearbox I B Input & Output Shafts (Aligned) y M y f(t) Figure 1: Mechanical assembly. a. Draw all the free-body diagrams and then derive the system's equations. (Motivate all steps performed.) b. Draw the state diagram of the system. (Avoid using differentiators.) (8 marks) (12 marks) A mechanical system consists of a mass M, a damper B, two springs and an ideal gearbox (i.e. negligible inertia and friction) as shown in Figure 1. An external force f(t) is exerted on the mass. For the gearbox, an input angular displacement of produces an output angular displacement of 0o =20. At rest with no external force applied, 0,0 = 0 rad. The input and output levers ('arms') connected rigidly to the input and output shafts of the gearbox, respectively, are both of unit length and have negligible mass. Both springs, one (with Hooke's constant K) connected to M and the other (with Hooke's constant K) connected to the output lever of the gearbox, are rigidly attached to the wall on the left. Both the wall and gearbox are inertially stationary. Assume the applied force to be always sufficiently small to ensure that the displacement 12 remains very small. Output & Input Levers K www ee Gearbox I B Input & Output Shafts (Aligned) y M y f(t) Figure 1: Mechanical assembly. a. Draw all the free-body diagrams and then derive the system's equations. (Motivate all steps performed.) b. Draw the state diagram of the system. (Avoid using differentiators.) (8 marks) (12 marks)
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mechanical engineering questions
-
3. Find the eigenfunctions for the Helmholtz equation dy +ky=0 dx subject to the boundary conditions at x = 0 and y=0 y+3y' = 0 at x = L. Show graphically that this leads to a discrete set of...
-
Read and answer the question below. EMBRACE DEMOGRAPHICS AND SOCIETAL CHANGES Using Differences to Drive Value Force 7: Demographics and Societal Changes. One of the most important forces that is...
-
s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...
-
Player A has a $1 bill and a $20 bill, and player B has a $5 bill and a $10 bill. Each player will select a bill from the other player without knowing what bill the other player selected. If the...
-
a. For each of the following pairs of reactions, indicate which one has the more favorable equilibrium constant (that is, which one most favors products): 1. 2. b. Which of the four reactions has the...
-
In an era in which mass media is but a thrall of its corporate masters, the amateurish _______ of commercials for local businesses provide a tonic for the slick homogeneity of most advertising. a....
-
Baycom Corporation's comparative balance sheet is provided in the Working Papers. Work independently to complete the following problem. 1. Complete the comparative balance sheet using trend analysis....
-
Equipment acquired on January 5, 2009, at a cost of $380,000, has an estimated useful life of 16 years, has an estimated residual value of $40,000, and is depreciated by the straight-line method. a....
-
For the period from 2023 to 2024, a company reports the following: Percentage change in sales 40% increase Percentage change in cost of goods sold 10% increase Percentage change in gross profit 20%...
-
Low Crop Prices Drag Farm Towns Down with Them: Low wheat, corn, and soybean prices mean another bad year for many Midwest farmers. In response to the above newspaper headline, what government action...
-
Consider the following program. 1: x = 5 2: if y 1 goto Label3 3: Labell: 4: ww + 1 5: if y 2 goto Label3 6: Label2: 7: q = 3 8: if z < 1 goto Labell 9: Label3: 10: w: := 2 11: if z 1 goto Label2 12:...
-
Two students are named to present their work from a class of 12 students: 4 from electrical department, 5 from telecommunication department and 3 from computer department. Let X denote the number of...
-
A small town in S. America had been plagued, thousands of people were dying of yellow fever. The task was to find the cause and eradicate it. Two approaches used were: Microscopic research on the...
-
How do effective change management strategies mitigate resistance and foster buy-in among stakeholders, ensuring smooth transitions and minimizing disruptions to established workflows and routines ?
-
i. Suggest at least THREE (3) kinds of analytics and machine learning algorithms that Champo Carpets can use to solve their problems, and in general, for value creation. ii. Explain the data strategy...
-
In your program, add comments that describe in English what your program does. Begin by writing your header and main program. Declare your variables, define their type, and use them. Make a list of...
-
CorpCo gathered the following information as of the end of the current fiscal year: Dividends on common stock Market price per share of common stock Shares of common stock outstanding Dividends on...
-
A copper sphere of 10-mm diameter, initially at a prescribed elevated temperature T;, is quenched in a saturated (1 atm) water bath. Using the lumped capacitance method, estimate the time for the...
-
Consider again the design for Example 10.4. Using a system as shown and the compensator determined in Equation (10.46), select an appropriate prefilter. Compare the response of the system with and...
-
A hydrobot is under consideration for remote exploration under the ice of Europa, a moon of the giant planet Jupiter. Figure DP4.6(a) shows one artistic version of the mission. The hydrobot is a...
-
Consider the control of the robot shown in Figure P3.18.The motor turning at the elbow moves the wrist through the forearm, which has some flexibility as shown [16]. The spring has a spring constant...
-
How is the average rate of return computed for capital investment analysis, assuming that the effect of straight-line depreciation on the amount of the investment is considered?
-
Which method of evaluating capital investment proposals reduces their expected future net cash flows to present values and compares the total present values to the amount of the investment?
-
Which two methods of capital investment analysis can be described as present value methods?
Study smarter with the SolutionInn App