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Simple Harmonic Motion

Simple Harmonic Motion. Physics 12. Joke of the day:. Is it June yet?. Simple Harmonic Motion:. Any motion that repeats itself precisely over equal periods of time is called periodic motion

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Simple Harmonic Motion

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  1. Simple Harmonic Motion Physics 12

  2. Joke of the day: • Is it June yet?

  3. Simple Harmonic Motion: • Any motion that repeats itself precisely over equal periods of time is called periodic motion • If that periodic motion is generated by a linear restoring force then it is simple harmonic motion (SHM).

  4. SHM Examples:

  5. Review: • Period (T) is the time for one complete oscillation. • Unit = seconds • Frequency (f) is the number of complete oscillations per second. • Units = Hertz (s-1 or 1/seconds)

  6. Photo by Mark Tippens Restoring force: • will tend to bring the system back toward equilibrium. • is a function only of position of the mass or particle. • is always directed back toward the equilibrium position of the system. A TRAMPOLINE exerts a restoring force on the jumper that is directly proportional to the average force required to displace the mat.

  7. More SHM: Displacement: distance from equilibrium. Amplitude: maximum displacement

  8. Review: Hooke’s Law: • F =restoring force of spring (N) • (-) because the force acts in opposite direction of the displacement and the applied force • K = spring constant (N/m) • Each spring has it’s own constant • x = distance that the spring has been extended or compressed (m) F = -kx

  9. Springs are like Waves! The amplitude, A, of a wave is the same as the displacement ,x, of a spring. Both are in meters. CREST Equilibrium Line Trough

  10. Review: Elastic Potential Energy: • Symbol: Ee • k = spring constant (N/m) • X= length of extension or compression (m) • Units = N·m or J Ee = ½ kx2

  11. Conservation of Energy in Springs:

  12. Total energy of mass and spring system: • At any position (x) the total energy is: • At either end, the mass stops, so velocity =0, also all elastic potential energy • At equilibrium, x=0 so all kinetic energy

  13. Period of mass on spring:

  14. Example 1: • If you stretch a spring a distance of 12.0cm from its rest length and release it. A 125g mass on the end of the spring completes exactly 20 cycles in 15.5 seconds. Find • The period • The force constant of the spring • The total energy of the system • The maximum speed of the mass • The speed of the mass when it is 10.0cm from the equilibrium

  15. Period of a pendulum:

  16. Example 2: • Find the period of a pendulum with a 2.45kg bob and having a length of 1.36m. By what would you have to increase the length in order to double the period?

  17. Try it : • What is the frequency of a pendulum of length 0.75m that is setup on the surface of Mars where the acceleration due to gravity is about 1/3 of that on Earth? • Page 608 • Questions 1-4 • Page 614 • Questions 5-8 (Answer:0.33hz)

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