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Slide 1

Introduction to Oscillations and Simple Harmonic Motion

Taldykorgan, KZ

NIS Grade 11 Physics

Slide 2

Describe examples of free oscillations.

Describe the conditions of Simple Harmonic Motion.

Apply Hooke’s Law for objects moving with simple harmonic motion.

Describe the motion of pendulums and calculate the length required to produce a given frequency.

Slide 3

Any periodic back and forth motion produced by a restoring force that is directly proportional to the displacement and in the opposite direction. The displacement centers around an equilibrium position.

Slide 4

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When the restoring force has the mathematical form F = –kx, the type of friction-free motion illustrated in the figure is designated as “simple harmonic motion.”

Slide 5

One of the simplest type of simple harmonic motion is called Hooke's Law. This is primarily in reference to SPRINGS.

The negative sign only tells us that “F” is what is called a RESTORING FORCE, in that it works in the OPPOSITE direction of the displacement.

Slide 6

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The maximum displacement from equilibrium is the amplitude ‘A’ of the motion. The shape of this graph is characteristic of simple harmonic motion and is called “sinusoidal,” because it has the shape of a trigonometric sine or cosine function.

Sin or Cos function depends on the starting position of the SHM.

The choice of using a cosine in this equation is arbitrary. Other valid formulations are: x = A sin(ωt + φ)

Slide 7

The amplitude, A, of a wave is the same as the displacement ,x, of a spring. Both are in meters.

CREST

Trough

Equilibrium Line

Period, T, is the time for ONE COMPLETE oscillation (One crest and trough). Oscillations could also be called vibrations and cycles. In the wave above we have 1.75 cycles or waves or vibrations or oscillations.

Ts=sec/cycle. Let’s assume that the wave crosses the equilibrium line in one second intervals. T =3.5 seconds/1.75 cycles. T = 2 sec.

Slide 8

The FREQUENCY of a wave is the inverse of the PERIOD. That means that the frequency is the number of cycles per sec. The commonly used unit is HERTZ (Hz).

- Objectives
- Definition: Simple Harmonic Motion
- Springs – Hooke’s Law
- Springs are like Waves and Circles
- Frequency
- The period and frequency of a wave
- Energy and Simple Harmonic Motion
- Definition of elastic potential energy
- Pendulums
- SHM and Uniform Circular Motion
- The Pendulum
- The Reference Circle
- Velocity in SHM
- Acceleration Reference Circle

- Newton’s Law of Gravity
- Ch 9 Nuclear Radiation
- Sensory and Motor Mechanisms
- History of Modern Astronomy
- Radioactivity and Nuclear Reactions
- Buoyancy
- Resource Acquisition and Transport in Vascular Plants

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