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    Simple Harmonic Motion Ph202/Note01/17.02.2009

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    nhc2009
    1) Simple harmonic motion is the oscillatory motion of a particle about a fixed point due to a restoring force proportional to the displacement from that point. 2) The differential equation describing simple harmonic motion along the x-axis is d2x/dt2 + kx = 0, where k is the force constant and m is the mass of the particle. 3) The period of oscillation T is equal to 2π/ω, where ω is the angular frequency. The phase of the motion, determined by ωt + α, completely describes the displacement and velocity of the particle at any time t.

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    Simple Harmonic Motion Ph202/Note01/17.02.2009

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    nhc2009
    24 views2 pages
    1) Simple harmonic motion is the oscillatory motion of a particle about a fixed point due to a restoring force proportional to the displacement from that point. 2) The differential equation describing simple harmonic motion along the x-axis is d2x/dt2 + kx = 0, where k is the force constant and m is the mass of the particle. 3) The period of oscillation T is equal to 2π/ω, where ω is the angular frequency. The phase of the motion, determined by ωt + α, completely describes the displacement and velocity of the particle at any time t.

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    Note01(17.01.2009).pdf

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    1) Simple harmonic motion is the oscillatory motion of a particle about a fixed point due to a restoring force proportional to the displacement from that point. 2) The differential equation describing simple harmonic motion along the x-axis is d2x/dt2 + kx = 0, where k is the force constant and m is the mass of the particle. 3) The period of oscillation T is equal to 2π/ω, where ω is the angular frequency. The phase of the motion, determined by ωt + α, completely describes the displacement and velocity of the particle at any time t.

    Copyright:

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

    Simple Harmonic Motion Ph202/Note01/17.02.2009

    Uploaded by

    nhc2009
    1) Simple harmonic motion is the oscillatory motion of a particle about a fixed point due to a restoring force proportional to the displacement from that point. 2) The differential equation describing simple harmonic motion along the x-axis is d2x/dt2 + kx = 0, where k is the force constant and m is the mass of the particle. 3) The period of oscillation T is equal to 2π/ω, where ω is the angular frequency. The phase of the motion, determined by ωt + α, completely describes the displacement and velocity of the particle at any time t.

    Copyright:

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

    1

    SIMPLE HARMONIC MOTION

    PH202/Note01/17.02.2009

    Definition
    A particle is said to execute a simple harmonic motion about a fixed point if it experiences a force
    which is always directed toward the fixed point and the magnitude of the force is proportional to the
    magnitude of displacement from the fixed point.

    O: fixed point; : displacement of the particle from the fixed point; : simple harmonic force
    From the definition,
    =

    If the simple harmonic motion is along the x-axis,


    = .
    The differential equation of simple harmonic motion along the x-axis is given by:
    2

    2 + = 0, m being the mass of the particle.


    2

    Or 2 + 2 = 0, 2 = , : angular frequency of shm


    The solution to this equation is of the form:
    = sin + = cos +
    A: amplitude; : angular frequency; : initial phase .

    = /2

    The Geometrical Definition of Simple Harmonic Motion

    Q: reference point which moves on the circle with angular speed .


    Physical Significance of
    Let T: the time period of shm.
    To show that =

    Let us look at the reference circle. At t=t the reference point Q is shown on the circle. The particle P
    will complete one oscillation when the point Q completes one rotation. Since the point Q has an
    angular speed , it will complete one rotation in 2/ seconds.
    So T=2/.
    Or =

    / .

    The phase of the motion


    The displacement and velocity of a particle at time t is completely determined by the quantity
    (t+). This quantity is called the phase of the motion.

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