Simple Harmonic Motion

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# Simple Harmonic Motion - PowerPoint PPT Presentation

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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Presentation Transcript

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

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.

Springs

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

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

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.

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

Amplitude

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

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.

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

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.