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KING FAISAL UNIVERSITY

COLLEGE OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

Course Code / Title: ME 312 – Mechanical Vibrations

Instructor: Dr. Mohammed Saber

Exam: QUIZ √MIDETRM 1 FINAL TOTAL: 10 Marks Semester / Year: Spring 2015 Date: September 15, 2015 Duration: 45 min

EXAM POLICY AND ETHICS:

during the exam, an absolute silence is required. All kinds of communication with the other students are strictly forbidden.

Turn your mobile phone off.

Answer all the questions and Problems.

QUESTIONS / STUDENT OUTCOMES: This exam covers/targets the following student outcomes (SOs):

SO (a): An ability to apply knowledge of mathematics, science, and engineering

SO (c):an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical,

health and safety, manufacturability, and sustainability SO (e):an ability to identify, formulate, and solve engineering problems

Q1 Q2 Total*

SO (a) /2 /3 /5

SO (c) /4 /6 /10

TOTAL /6 /9 /15

*15 points = 10 Marks

FEEDBACK SUMMARY: ………………………………………………………………………………………………………………………………………....................

........…………………………………………………………………………………………………………………………………………………

STUDENT IDENTIFICATION: Name: ……………………………………………. ID: ………….…….…………… Signature: ……..……………………. By signing this form, the student recognizes that he understands and accepts the exam policy and ethics. He recognizes also that if he

does not respect these ethical rules, the professor will take the appropriate measures including exclusion from the exam.

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Useful Relations

𝜔𝑑 = 𝜔𝑛 1 − 𝜁2 𝐶𝑐𝑟 = 2 𝑘𝑚 𝑥 𝑡 = 𝐴𝑒−𝜁𝜔𝑛 𝑡 Sin(𝜔𝑑𝑡 + ∅)

𝐴 = (𝑣0+𝜁𝜔𝑛𝑥0)2+ 𝑥0𝜔𝑑

2

𝜔𝑑2 ∅ = tan−1 𝑥0𝜔𝑑

𝑣0+𝜁𝜔𝑛𝑥0

Question One [6 Points]:

A)The figure below is the response of a spring-mass- dashpot system has a 2Kg mass and the damping ratio of 0.1 and vo=4 mm/s.

1-Determine the values of the following:- [5 points]

1- T (s) 6- c (kg/s)

2- fd (Hz) 7- Φ (rad)

3- ωd (rad/s) 8- A (mm)

4- ωn (rad/s) 9-Max. Velocity (mm/s)

5- K(N/m) 10-Max. Acceleration (mm/s2)

2-What is the time needed to obtain -0.1 mm displacement? [1 point]

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Question Two [9 points]: A) Determine the stiffness of spring K2 such that a mass of 15kg has natural frequency of 10 rad/s. Stiffness of springs is in KN/m. [4 points]

3 3

K2 4

3 3

2

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B) Derive the equation of motion for the system shown, using Newton’s second law, and determine the natural

frequency of the system. [5 points]

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