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C8 - Applied Science Department(ASD Centre for Foundation...

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FOSEE , MULTIMEDIA UNIVERSITY (436821-T) MELAKA CAMPUS, JALAN AYER KEROH LAMA, 75450 MELAKA, MALAYSIA. Tel 606 252 3594 Fax 606 231 8799 URL: http://fosee.mmu.edu.my/~asd/ PPH0075 Physics 1 Foundation in Engineering ONLINE NOTES Chapter 8 Oscillations Applied Science Department (ASD) Centre for Foundation Studies and Extension Education (FOSEE)
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PPH0075 Physics 1 Chapter 8 ______________________________________________________________________________________ ASD2008/09 1/ 12 Error! Mass-spring system Simple Pendulum system Period, T Frequency, f Equilibrium position Displacement, x Amplitude, A Acceleration, a Damped Oscillation Forced Oscillation Resonance of SHM Velocity, v Energy of SHM Chapter 8 Oscillations What is Oscillation/SHM? Definition General properties of SHM SHM applied on IDEAL physical system SHM applied on REAL physical system
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PPH0075 Physics 1 Chapter 8 ______________________________________________________________________________________ ASD2008/09 2/ 12 8.1 OBJECTIVES At the end of this chapter, students should be able to: a. Explain what is meant by Simple Harmonic Motion. b. Understand and use the terms amplitude, period, frequency, angular frequency and phase difference and express the period in terms of both frequency and angular frequency for both mass-spring system and simple pendulum. c. Describe phase lead, phase lag, antiphase and inphase. d. Describe the interchange between kinetic and potential energy during simple harmonic motion. e. Explain what is a resonance and give example. 8.2 TYPES OF MOTION a. Motion in which a body moves from one place to another with respect to time, e.g a moving train. b. Motion in which a body moves about a fixed point, back and forth over the same path, e.g the bob of a simple pendulum. This type of motion is called oscillatory motion. 8.3 DEFINITION OF SOME TERMS a. Periodic Motion This is when motion takes place at equal intervals of time; eg, planetary motion, simple pendulum motion, etc. b. Period ( T ) Time taken for one complete oscillation. c. Frequency ( f ) Number of oscillations per second. It is measured in hertz (Hz) Frequency and period are related to each other by f = 1 / T . d. Equilibrium ( or Neutral ) Position The position at which no net force acts on the oscillating mass. e. Displacement The distance of the oscillating mass from its equilibrium position, at any instant. f. Amplitude The maximum displacement of the oscillating mass from its equilibrium position. g. Phase Two particles are said to be oscillating in phase if they are in the same state of disturbance at the same time. Otherwise, they are said to be oscillating out of phase. For mechanical oscillation to be possible, there must be a restoring force opposite to the displacement.
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PPH0075 Physics 1 Chapter 8 ______________________________________________________________________________________ ASD2008/09 3/ 12 8.4 SIMPLE HARMONIC MOTION In simple harmonic motion (SHM), the restoring force, F , is proportional to the displacement, x , but directed opposite to it. Mathematically, F = - k x where k is a constant . If the only force acting on the oscillating mass is the restoring force then by Newton’s Second Law , F = ma Here, ma = - k x or a = -k / m x Or a α -x Where 2 2 dt x d a = This is a second-order differential equation easily solvable if we make the constant ω 2 , where ω is known as the angular frequency.
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