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    Mass of A Simple Pendulum: Small-Angle Approximation

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    yashsodhani
    The document discusses the mass of a simple pendulum and its motion as it relates to simple harmonic motion. For small oscillations, the period of a pendulum is independent of its mass and amplitude but depends on the length of the pendulum and gravitational acceleration. The approximation of simple harmonic motion is accurate for small angles of displacement due to the relationship between angular acceleration and the sine of the displacement angle.

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    Mass of A Simple Pendulum: Small-Angle Approximation

    Uploaded by

    yashsodhani
    16 views2 pages
    The document discusses the mass of a simple pendulum and its motion as it relates to simple harmonic motion. For small oscillations, the period of a pendulum is independent of its mass and amplitude but depends on the length of the pendulum and gravitational acceleration. The approximation of simple harmonic motion is accurate for small angles of displacement due to the relationship between angular acceleration and the sine of the displacement angle.

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    SHM

    Original Title

    I

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    The document discusses the mass of a simple pendulum and its motion as it relates to simple harmonic motion. For small oscillations, the period of a pendulum is independent of its mass and amplitude but depends on the length of the pendulum and gravitational acceleration. The approximation of simple harmonic motion is accurate for small angles of displacement due to the relationship between angular acceleration and the sine of the displacement angle.

    Copyright:

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

    Mass of A Simple Pendulum: Small-Angle Approximation

    Uploaded by

    yashsodhani
    The document discusses the mass of a simple pendulum and its motion as it relates to simple harmonic motion. For small oscillations, the period of a pendulum is independent of its mass and amplitude but depends on the length of the pendulum and gravitational acceleration. The approximation of simple harmonic motion is accurate for small angles of displacement due to the relationship between angular acceleration and the sine of the displacement angle.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
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    SHM

    Mass of a simple pendulum[edit]

    The motion of an undampedpendulumapproximates to simple harmonic motion if the angle of oscillation is


    small.

    In the small-angle approximation, the motion of a simple pendulum is approximated by simple


    harmonic motion. The period of a mass attached to a pendulum of length with gravitational
    acceleration g is given by

    This shows that the period of oscillation is independent of the amplitude and mass of the
    pendulum but not of the acceleration due to gravity (g), therefore a pendulum of the same
    length on the Moon would swing more slowly due to the Moon's lower gravitational field
    strength.
    This approximation is accurate only for small angles because of the expression for angular
    acceleration being proportional to the sine of the displacement angle:

    where

    is the moment of inertia. When is small, sin and therefore the expression

    becomes

    SHM

    which makes angular acceleration directly proportional to , satisfying the definition


    of simple harmonic motion.

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