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    Mid I

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    azooz
    The document contains a mid-term exam for a mechanical vibrations course. It consists of 3 problems: 1) finding the response of a single degree of freedom building frame subjected to a triangular pulse loading, 2) deriving the equation of motion and finding the steady state response of a lever system, and 3) determining values of stiffness and damping that will produce a specified damped natural frequency and decay rate for a mass-spring-damper system. Formulas and steps relevant to solving vibration and oscillation problems are also presented.

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    Mid I

    Uploaded by

    azooz
    18 views4 pages
    The document contains a mid-term exam for a mechanical vibrations course. It consists of 3 problems: 1) finding the response of a single degree of freedom building frame subjected to a triangular pulse loading, 2) deriving the equation of motion and finding the steady state response of a lever system, and 3) determining values of stiffness and damping that will produce a specified damped natural frequency and decay rate for a mass-spring-damper system. Formulas and steps relevant to solving vibration and oscillation problems are also presented.

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    MID I

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    The document contains a mid-term exam for a mechanical vibrations course. It consists of 3 problems: 1) finding the response of a single degree of freedom building frame subjected to a triangular pulse loading, 2) deriving the equation of motion and finding the steady state response of a lever system, and 3) determining values of stiffness and damping that will produce a specified damped natural frequency and decay rate for a mass-spring-damper system. Formulas and steps relevant to solving vibration and oscillation problems are also presented.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    18 views4 pages

    Mid I

    Uploaded by

    azooz
    The document contains a mid-term exam for a mechanical vibrations course. It consists of 3 problems: 1) finding the response of a single degree of freedom building frame subjected to a triangular pulse loading, 2) deriving the equation of motion and finding the steady state response of a lever system, and 3) determining values of stiffness and damping that will produce a specified damped natural frequency and decay rate for a mass-spring-damper system. Formulas and steps relevant to solving vibration and oscillation problems are also presented.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 4

    King Saud University

    Mechanical Engineering Department


    MID-TERM EXAM I - ME 462-Mechanical Vibrations

    Problem 1

    A building frame is modeled as an undamped single degree of freedom system (Fig. a). Find
    the response of the frame if it is subjected to a blast loading represented by the triangular
    pulse as shown in (Fig. b).
    Problem 2

    (a) Derive the equation of motion for the system shown in terms of the coordinate x .
    (b) Find the steady state response of the system.
    Assume small oscillations. The lever AOC has mass moment of inertia J O .
    Problem 3

    Determine the values of k and c for the system shown if the damped period of vibration is to
    be 0.3 s and the amplitude of vibration of the system decays to half of its initial value in 6
    cycles.
    J 0  2.4 kg.m 2 , m  5 kg, r1  0.2 m, r2  0.4 m.
    t
    1
    m n 0
    x(t )  F ( ) sin  n (t   ) d

    1
     sin  n (t   )d 
    n
    [cos  n (t   )]

     cos  n (t   ) sin  n (t   )
     sin  n (t   )d 
    n

     n2
    F0
    X 
    k  m   c   2 2 2 2
    1/ 2

     c 
      tan 1  2 
     k  m 

    cc  2m n
    c
    
    cc
    d  n 1   2
    2
    d 
    d
    x1
     e n n d
    xn 1

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