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Energy and simple armonic motion
Energy and simple armonic motion
Energy and simple armonic motion
Energy and simple armonic motion
Energy and simple armonic motion
Energy and simple armonic motion
Energy and simple armonic motion
Energy and simple armonic motion
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Energy and simple armonic motion

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IBDP Physucs topic 4.2

IBDP Physucs topic 4.2

Published in: Technology, Education
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  • 1. Oscillations and Waves Topic 4.2 Energy changes during SHM
  • 2. <ul><li>The frequency of simple harmonic motion like a mass on a spring is determined by the mass m and the stiffness of the spring expressed in terms of a spring constant k ( see Hooke’s Law): </li></ul>
  • 3. Mass on spring resonance <ul><li>A mass on a spring has a single resonant frequency determined by its spring constant k and the mass m. Using Hooke’s law and neglecting damping and the mass of the spring, Newton’s second law gives the equation of motion: </li></ul>the expression for the resonant vibrational frequency: This kind of motion is called simple harmonic motion and the system a simple harmonic oscillator.
  • 4. Mass on spring: motion sequence <ul><li>A mass on a spring will trace out a sinusoidal pattern as a function of time, as will any object vibrating in simple harmonic motion. One way to visualize this pattern is to walk in a straight line at constant speed while carrying the vibrating mass. Then the mass will trace out a sinusoidal path in space as well as time. </li></ul>
  • 5. Energy in mass on spring <ul><li>The simple harmonic motion of a mass on a spring is an example of an energy transformation between potential energy and kinetic energy. In the example below, it is assumed that 2 joules of work has been done to set the mass in motion. </li></ul>
  • 6. Potential energy At extension x:
  • 7. Kinetic energy At extension x:
  • 8. Total energy Total energy

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