EG-260 Continuous Assessment 1

Warning: Failure to follow these instructions will result in zero mark for the entire assessment. These instructions are purposefully very detailed and highlight common mistakes that have been seen in the past. My goal is to make sure that you communicate your answers to this assessment in the correct manner so that I can assign you the correct marks. It is therefore crucial that you read, understand and follow these instructions.

Instructions:

• This assessment must be solved and submitted individually. The submission deadline is:

23.59 on Thursday 9 March 2017

• Use numerical values for the parameters corresponding to your student number from xls file available on blackboard.

• Solve all of the questions in this assessment using the parameters that are assigned to your student number. Remember: Each answer that you will obtain WILL be a numerical value. When solving the questions, maintain highest possible decimal points. Your final answer should be rounded to 4 decimal places (done automatically in the xls file).

• Submit the Excel file (xls) in Blackboard.

• IN ADDITION to the xls file, you MUST submit a SINGLE file containing the supporting work. This file should show how you have solved the problems. This is the evidence that you obtained the numerical results yourself. You can type your solution in WORD or SCAN your handwritten work. Either way, submission should be a PDF file. Remember, this FILE NAME must be MySolution.pdf. Do NOT submit separate files for different parts of your solution. Avoid JPG, TIF or other image files if possible.

• Numerical answers in both files must agree with each other. In case of any discrepancies, the answers in xls will be used for marking.

• Unlike the final exam, no method marks is available for this assessment. You have to get correct numerical values and enter it correctly as described above. This is because, unlike the final exam, you have one full week to solve the two problems.

• Please submit the two files ONLY once.

• Question 1: An inverted pendulum oscillator of length L [m] and mass m [kg] is attached by springs. Two springs of stiffness values k1 and k2 [N/m] are arranged in parallel and series respectively as shown below:

Important: The values of L, m, k1 and k2 in SI units are given for your student number in the excel file CA1_Parameters.xls. Use an equivalent spring in deriving the equation of motion and consider the weight of the mass. Take gravitational acceleration constant as 9.8100 [m/s2]. All answers must be in numerical format and in SI units.

Case 1: springs in parallel                      Case 2: springs in series

1. Calculate the equivalent spring stiffness for case 1 and enter the numerical value to the designated cell in the Excel file.                                     (5 Marks)
2. Calculate the equivalent spring stiffness for case 2 and enter the numerical value to the designated cell in the Excel file.                                                               (5 Marks)
3. Assuming the rotation is small, obtain the equation of motion. From this, calculate the natural frequency in rad/sec for case 1 and enter the numerical value to the designated cell in the Excel file.              (15 Marks)
4. From the equation of motion, calculate the natural frequency in rad/sec for case 2 and enter the numerical value to the designated cell in the Excel file. (15 Marks)
5. Assuming k2 = 2k1, obtain the value of k1 (in N/m) for the system to be stable for case 1 and enter the numerical value to the designated cell in the Excel file. (5 Marks)
6. Assuming k2 = 2k1, obtain the value of k1 (in N/m) for the system to be stable for case 2 and enter the numerical value to the designated cell in the Excel file.      (5 Marks)

Question 2: A vibrating system consisting of a weight of W [N] and a spring stiffness of k [N/m] is viscously damped such that the ratio of any two consecutive amplitudes is 10 to y. Determine:

1. Log decrement () and enter the numerical value to the designated cell in the Excel file.                        (10 Marks)
2. Damping factor () and enter the numerical value to the designated cell in the Excel file.                   (10 Marks)
3. Damped natural frequency () in (rad/sec) and enter the numerical value to the designated cell in the Excel file.    (15 Marks)
4. Damping constant (c) and enter the numerical value to the designated cell in the Excel file.                (15 Marks)

Hint: The values of W, k, and y in SI units are given for your student number in the Excel file CA1_Parameters.xls. Take gravitational acceleration constant as 9.8100 [m/s2]. All answers must be in numerical format and in SI units.

Reminder: Failure to follow the instructions will result in zero marks even if you obtained correct answers! For the sake of fairness, no exceptions will be allowed. Unless you are ABSOLUTELY sure that your submission is according to the instructions, please do not upload it in the blackboard.