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Simple Harmonic Motion

Explore the commonalities between mass on a spring and pendulum, learn about periodic motion, equilibrium forces, and more. Discover the relationships between amplitude, period, and oscillations in Simple Harmonic Motion. Dive into equations, frequency, and energy in oscillatory systems.

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Simple Harmonic Motion

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  1. Simple Harmonic Motion AP Physics

  2. Examples: Mass on a spring Pendulum What do they both have in common? What is periodic motion?

  3. At equilibrium, net force is zero. The acceleration is also zero at equilibrium. Where does this happen for: A pendulum? A mass on a spring? The graph on the right? Equilibrium and SHM

  4. SHM is like Waves Crest Equilibrium Line The amplitude, A, of a wave is the same as the displacement ,x, of a spring. Both are in meters. Trough Period, T, is the time for one revolution or in the case of springs the time for ONE COMPLETE oscillation (One crest and trough). Oscillations could also be called vibrations and cycles.

  5. Simple Harmonic Motion • Back and forth motion that is caused by a force that is directly proportional to the displacement. The displacement centers around an equilibrium position. Also known as Periodic Motion. • Pendulum • Mass on a Spring • Uniform Circular Motion • Harmonic Oscillator: object undergoing harmonic motion

  6. SHM and Uniform Circular Motion • Springs and Waves behave very similar to objects that move in circles. • The radius of the circle is symbolic of the displacement, x, of a spring or the amplitude, A, of a wave.

  7. A simple pendulum consists of a mass, called a bob, suspended by a string or rod of length L. String or rod is considered massless. The time to complete one full cycle is a period. What is the period (T) of the pendulum in the room? Simple Pendulum

  8. Pendulum Mass does not effect the motion of the pendulum What does effect the motion of a pendulum? ‘g’ Length of pendulum Mass on a Spring Gravity does not effect the motion of the mass on a spring system What does effect the motion of the mass on a spring? Mass Spring constant Equations: Pendulum and Mass on a Spring

  9. Frequency (f) The number of cycles completed in a period of time. Total cycles/total time Units: Hertz (Hz) Hz = 1/sec Period (T) The time to complete one cycle. Total time/total cycles Units: seconds Frequency and Period

  10. SHM Motion is continuous. DHM Motion slows to a stop over time. The amplitude of motion decreases with time. Link to Harmonic Motion Damped Harmonic Motion

  11. Example: Energy and SHM • A 200 g mass is attached to a spring that undergoes simple harmonic motion with a frequency of 4 Hz. If the total energy of the system is 2.0 J, find: • The spring constant. • The amplitude of the motion. 126.3 N/m 0.18 m

  12. Combinations of Springs Parallel Series Less stiff system 1/K = 1/K + 1/K • Stiffer system • Add to get equivalent Two springs are combined. The spring constants of each are 100 N/kg and 200 N/kg, respectively. What is the equivalent spring constant when combined in series? in parallel?

  13. Set-up

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