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Guilherme Mazui

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What is the Difference Between Simple Harmonic Motion and Periodic Motion?

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The main difference between simple harmonic motion and periodic motion lies in the nature of the motion and the forces involved. Here are the key differences:

Simple Harmonic Motion:

  1. In simple harmonic motion, the displacement of the object is always in the opposite direction of the restoring force.
  2. The acceleration of the object is directly proportional to the displacement and acts in the opposite direction, which means the motion can be described by a second-order linear differential equation.
  3. The period of oscillation does not depend on the amplitude of the motion, and the motion can be described using trigonometric functions.

Periodic Motion:

  1. In periodic motion, the displacement of the object may or may not be in the direction of the restoring force.
  2. The motion is oscillatory and repeats itself, but the acceleration of the object is not necessarily directly proportional to the displacement and acting in the opposite direction.
  3. The period of oscillation can vary depending on the amplitude of the motion, and the motion can be described using various mathematical functions.

In summary, simple harmonic motion is a specific type of periodic motion where the acceleration of the object is directly proportional to the displacement and acts in the opposite direction. In contrast, periodic motion is a more general term that refers to any oscillatory motion, including simple harmonic motion.

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  • What is the Difference Between Simple Harmonic Motion and Periodic Motion?
  • Comparative Table: Simple Harmonic Motion vs Periodic Motion

    • Comparative Table: Simple Harmonic Motion vs Periodic Motion

    Here is a table comparing the differences between simple harmonic motion and periodic motion:

    Feature Simple Harmonic Motion (SHM) Periodic Motion
    Definition An oscillatory motion where the restoring force is directly proportional to the displacement of the body from its mean position, and the acceleration is given by Hooke's Law. A motion that repeats itself after an equal interval of time, with no equilibrium position and no specific restoring force.
    Equilibrium A stable equilibrium position exists. For example, the equilibrium position of a mass on a spring is the place where the mass is returned to its original position. There is no stable equilibrium position. Uniform circular motion is an example of periodic motion without an equilibrium position.
    Displacement Displacement in simple harmonic motion as a function of time is given by $$x(t)=X\cos\left(\frac{2\pi t}{T}\right),$$ where X is the amplitude of the motion. The displacement of the system does not vary with simple harmonic functions (sine or cosine).
    Velocity The velocity function for simple harmonic motion is given by $$v(t)=-v{\text{max}}\text{sin}\left(\frac{2\pi t}{T}\right),$$ where $$v{\text{max}} = \sqrt{\frac{k}{m}}X$$. The velocity function does not follow a simple harmonic function and may vary with other functions, like sine or cosine.
    Acceleration The acceleration function for simple harmonic motion is given by $$a(t)=-\frac{kX}{m}\cos\left(\frac{2\pi t}{T}\right)$$. The acceleration function does not follow a simple harmonic function and may vary with other functions, like sine or cosine.
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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.