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    Problem Set Unit-1A

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    Kool Prashant
    This document contains a problem set on forced vibration with questions on: 1) Deriving equations of motion for simple harmonic motion and damped oscillation using energy conservation and solving using complex forms. 2) Relating the mechanical system to AC circuits and defining mechanical impedance, resonance, power, power factor, and quality factor. 3) Plotting velocity amplitude vs frequency and analyzing phase relationships between applied force, displacement and velocity. 4) Calculating values like mechanical impedance, maximum amplitude and velocity for a driven telephone diaphragm. 5) Finding natural frequency, decay constant and quality factor for a given oscillator.

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    Problem Set Unit-1A

    Uploaded by

    Kool Prashant
    15 views2 pages
    This document contains a problem set on forced vibration with questions on: 1) Deriving equations of motion for simple harmonic motion and damped oscillation using energy conservation and solving using complex forms. 2) Relating the mechanical system to AC circuits and defining mechanical impedance, resonance, power, power factor, and quality factor. 3) Plotting velocity amplitude vs frequency and analyzing phase relationships between applied force, displacement and velocity. 4) Calculating values like mechanical impedance, maximum amplitude and velocity for a driven telephone diaphragm. 5) Finding natural frequency, decay constant and quality factor for a given oscillator.

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    This document contains a problem set on forced vibration with questions on: 1) Deriving equations of motion for simple harmonic motion and damped oscillation using energy conservation and solving using complex forms. 2) Relating the mechanical system to AC circuits and defining mechanical impedance, resonance, power, power factor, and quality factor. 3) Plotting velocity amplitude vs frequency and analyzing phase relationships between applied force, displacement and velocity. 4) Calculating values like mechanical impedance, maximum amplitude and velocity for a driven telephone diaphragm. 5) Finding natural frequency, decay constant and quality factor for a given oscillator.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    15 views2 pages

    Problem Set Unit-1A

    Uploaded by

    Kool Prashant
    This document contains a problem set on forced vibration with questions on: 1) Deriving equations of motion for simple harmonic motion and damped oscillation using energy conservation and solving using complex forms. 2) Relating the mechanical system to AC circuits and defining mechanical impedance, resonance, power, power factor, and quality factor. 3) Plotting velocity amplitude vs frequency and analyzing phase relationships between applied force, displacement and velocity. 4) Calculating values like mechanical impedance, maximum amplitude and velocity for a driven telephone diaphragm. 5) Finding natural frequency, decay constant and quality factor for a given oscillator.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    PH-1201

    Problem set for Unit-1A


    (Forced vibration)
    A. Theory
    1. Consider a particle executing SHM. Find out the equation of motion from energy
    conservation.
    2. What should be the form of equation of motion in case of damped oscillation and find the
    solution in case of low damping, critical damping and over damping.
    3. Solve the equation M.d2 x/dt2+Rm.dx/dt+S.x=F.cost for force vibration using complex
    form.
    4. Write the above equation in the form M.dv/dt + Rm.v + S.
    velocity at steady state.

    = F.cost and solve it for

    5. Point out the similarities between this mechanical system and an a.c. circuit.
    6.

    What is mechanical impedance? Is it real or complex quantity? Justify your answer.

    7. What is resonance? Find out the maximum displacement and velocity amplitude at
    resonance. Distinguish between the displacement resonance and velocity resonance in
    terms of energy.
    8. Defined power in force vibration. What is the average power at resonance? Is it the
    maximum value of average power which can be obtained by varying alone?
    9. Show that in steady state of force vibration and also at resonance the power dissipated per
    cycle is spent in overcoming the resistance.
    10. Defined power factor? What is the power factor at velocity resonance?
    11. What is sharpness of resonance? Find a measure for it.
    12. Defined half-power frequency, Quality factor and band-width.
    13. Plot the velocity amplitude as a function of and find the different components of the
    impedance at different region of the curve which are effective in controlling the velocity
    amplitude.
    14. What is the phase relation between applied force, displacement and the velocity at steady
    state? Show the variation of (phase angle between velocity and force) and (phase
    angle between displacement and force) with for two different Rm and justify your
    answer.

    B. Problem
    1. A telephone diaphragm of effective mass 1 g is acted on by a restoring force of 10 7 dynes
    per cm of displacement, a retarding force of 4*10 3 dynes per unit velocity (cm/s) and a
    driving force of 105 cos5t dynes. Find the values of its
    (a) Mechanical impedance
    (b) Mechanical reactance
    (c) Maximum possible amplitude
    (d) Maximum possible velocity
    (e) At what frequencies do (c) and (d) occur?
    (f) What is value of (b) at the frequency of (d)?
    (g) If the frequency of velocity resonance is sought to be reduced to half by changing the
    mass only, then what will be the new mass?
    2. An oscillator has a mass of 10 g, a retarding force of 100 dyne.s.cm-1 and a restoring
    force of 106 dune cm-1. Find its
    (a) Natural frequency
    (b) Decay constant
    (c) Quality factor (Q)

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