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Simple Harmonic Motion

Simple Harmonic Motion. What is Simple Harmonic Motion?. Simple harmonic motion (SHM) a type of wavelike motion that describes the behavior of many physical phenomena: a pendulum a bob attached to a spring low amplitude waves in air (sound), water, the ground

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Simple Harmonic Motion

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  1. Simple Harmonic Motion

  2. What is Simple Harmonic Motion? • Simple harmonic motion(SHM)a type of wavelike motion that describes the behavior of manyphysical phenomena: • a pendulum • a bob attached to a spring • low amplitude waves in air (sound), water, the ground • the electromagnetic field of laser light • vibration of a plucked guitar string • the electric current of most AC power supplies

  3. What is Simple Harmonic Motion? (cont.) • This wavelike motion is repetitive. • It is caused by a restoring force that acts in the opposite direction of the displacement.

  4. Springs • If we stretch a spring with a mass on the end and let it go, the mass will oscillate back and forth.

  5. Simple Pendulum • Under small displacements, the simple pendulum behaves as a harmonic oscillator. • the restoring force is a component of the bob’s weight. L Ft Fg,x mg Fg,y

  6. The period and frequency of a wave • The period (T) is the amount of time it takes a wave to go through 1 cycle. • Frequency (f )is the number of cycles per second.

  7. The period and frequency of a wave (cont.) • unit of a frequency =hertz(Hz) • Heinrich Hertz (1847-1894), discovered radio waves. f = 1 / T T = 1 / f

  8. Amplitude • The maximum displacement from some equilibrium (mid point) position.

  9. Period of a mass-spring in harmonic motion T = 2π √(m/k) • The period of a mass-spring system depends on the mass of the object and the spring constant.

  10. T = 2π√(m / k) k = ? Sample Problem The body of a 1275 kg car is supported on a frame by four springs. Two people riding in the car have a combined mass of 153 kg. When driven on a pothole in the road, the frame vibrates with a period of 0.84 s. For the first few seconds, the vibration approaches simple harmonic motion. Find the spring constant of a single spring. T= 0.84 s m = (1275 kg + 153 kg) / 4 = 357 kg T² = (4π²m) / k k = (4π²m) / T² k = [4π² (357 kg)] / (0.84 s)² = 2.00 x 104 N/m

  11. Period of a simple pendulum in harmonic motion T = 2π √(L/g) • The period of a simple pendulum depends on the string length and gravity.

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