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# Energy and simple armonic motion

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IBDP Physucs topic 4.2

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### Energy and simple armonic motion

1. 1. Oscillations and Waves Topic 4.2 Energy changes during SHM
2. 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. 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. 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. 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. 6. Potential energy At extension x:
7. 7. Kinetic energy At extension x:
8. 8. Total energy Total energy
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