A trolley of mass 'm' fixed onto a damper with a damping constant 'b' and onto...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A trolley of mass 'm' fixed onto a damper with a damping constant 'b' and onto serially connected springs having stiffness coefficients of 'ki' and 'k' respectively and is moving along a smooth surface under free-vibrational motion with an initial excitation of u(t). The x(t) defines as the displacement of the trolley. b fisi m Figure A1.1. a) Determine the governing differential equation of motion for the spring-mass-damper system shown in Figure A1.1. [06 marks] b) If x(t)= K.et, then determine the respective quadratic equation in terms of X. (K & R) [03 marks] c) Determine the roots of the equation mentioned in part (b), in terms of m, b and ki and k2. [02 marks] d) State the condition for critical damping w.r.t the equation in part (b). Determine the damping ratio ''. [04 marks] e) Assuming that the said system adheres to the standard oscillatory model, deduce damping ratio ' in terms of natural frequency . [03 marks] f) Express the roots of the quadratic equation in part (b) in terms of and con. [02 marks] g) Detern ine the roots of the quadratic equation in part (b) for an underdamped scenario. [03 marks] h) If b=0.75 Nsm, m= 0.5 kg & k = 80Nm, determine the damping ratio '' for the given system. [02 marks] A trolley of mass 'm' fixed onto a damper with a damping constant 'b' and onto serially connected springs having stiffness coefficients of 'ki' and 'k' respectively and is moving along a smooth surface under free-vibrational motion with an initial excitation of u(t). The x(t) defines as the displacement of the trolley. b fisi m Figure A1.1. a) Determine the governing differential equation of motion for the spring-mass-damper system shown in Figure A1.1. [06 marks] b) If x(t)= K.et, then determine the respective quadratic equation in terms of X. (K & R) [03 marks] c) Determine the roots of the equation mentioned in part (b), in terms of m, b and ki and k2. [02 marks] d) State the condition for critical damping w.r.t the equation in part (b). Determine the damping ratio ''. [04 marks] e) Assuming that the said system adheres to the standard oscillatory model, deduce damping ratio ' in terms of natural frequency . [03 marks] f) Express the roots of the quadratic equation in part (b) in terms of and con. [02 marks] g) Detern ine the roots of the quadratic equation in part (b) for an underdamped scenario. [03 marks] h) If b=0.75 Nsm, m= 0.5 kg & k = 80Nm, determine the damping ratio '' for the given system. [02 marks]
Expert Answer:
Related Book For
Posted Date:
Students also viewed these accounting questions
-
A particular oscillator satisfies the equation of motion i + 10 + 16x = 0 Q3.1 5 Points Find the damping constant b and the spring constant k in terms of m. Is the harmonic oscllator under-,...
-
A trolley of mass m is fixed to the end of a spring. The spring can be compressed and extended. The spring has a force constant k. The other end of the spring is attached to a vertical wall. The...
-
A light rigid rod of length 9L, shown in its static position in the figure below, is more connected at point O and carries masses M and 2m at the indicated position. The motion of the bar is...
-
Assume that global lightning on the Earth constitutes a constant current of 1.00 kA between the ground and an atmospheric layer at potential 260 kV. (a) Find the power of terrestrial lightning. (b)...
-
Discuss the major problems that arose in this development project and describe how Anderson should deal with them. Late Friday afternoon, T. N. (Ted) Anderson, director of disbursements for Consumer...
-
The Biscuit Manufacturing Company commenced business on 1 January Year 1 with capital of 22,000 contributed by the owner. It immediately paid cash for a biscuit machine costing 22,000. It was...
-
Suppose a trader buys a European Put on a share for \(\$ 4\). The stock price is \(\$ 53\) and the strike price is \(\$ 49\). (a) Under what circumstances will the trader make a profit? (b) Under...
-
Making a Decision as a Financial Analyst: Preparing and Analyzing a Balance Sheet Your best friend from home writes you a letter about an investment opportunity that has come her way. A company is...
-
Suggest one best practice recommendation for backbone design and explain why it's a best practice.
-
The director of RCM inc. plans to launch a new product. The initial investment in equipment and other fittings is $800,000. It's been a while since management thinking of launching this new product....
-
What are the three methods that are used to dispose of over/under absorbed overhead balances?
-
What do you think are the main differences between legal rules and other kinds of rules?
-
If senior management appointed you to chair a committee to adopt such a concept, whom would you include?
-
Should statutory exemptions for serving on a jury be declared illegal on a nationwide basis rather than letting each state choose whether to have this type of law?
-
Describe the recent key elements to legislative reform of the Medicare payment structure.
-
The campus food service would like to determine how many people eat in the student cafeteria. List the ways in which this information could be obtained. Which method is best?
-
A drug store (pharmacy) chain wants to raise $500,000 using two-month commercial paper. The net proceeds to the chain will be $497,500. What is the effective annual rate of this financing? Given what...
-
Smthe Co. makes furniture. The following data are taken from its production plans for the year. Required: 1. Determine the hazardous waste disposal cost per unit for chairs and for tables if costs...
-
In the system shown in Figure, the input is the displacement y and the output is the displacement x. When x = y = 0 the springs are at their free lengths. Derive the equation of motion. K C kz
-
Consider Example 10.6.3. Use the same gain values computed for the three cases in that example. a. Use MATLAB to plot the command response and the actuator response to the modified unit-step command...
-
The speed wi of the load is to be controlled with the torque T acting through a fluid coupling (see Figure P12.5). Design a compensator for the specific plant Gp (s) = 2 (s) / T (s) = 4 / s2 + 2s So...
-
The \(x\) component of the velocity of a car changes from \(-10 \mathrm{~m} / \mathrm{s}\) to \(-2.0 \mathrm{~m} / \mathrm{s}\) in \(10 \mathrm{~s}\). (a) Is the car traveling in the positive or...
-
The day after the incident described in Problem 44, the instructor finds herself in the same situation. This time, she tries a harder physics exercise. She keeps running at a constant \(6.0...
-
(a) A car is speeding up in the negative \(x\) direction. In what direction do \(\vec{a}\) and \(\vec{v}\) point? (b) To which of the four graphs in Figures 3 . 2 and 3 . 3 does the situation...
Study smarter with the SolutionInn App