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Lesson_Text_5.1 - 1 Lesson 5.1 Oscillations Lesson...

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1 Lesson 5.1 Oscillations Lesson Objectives: At the end of this lesson students will be able to (i) describe the characteristics of simple harmonic motion and derive a mathematical expression describing such a motion. (ii) Interpret the equation describing simple harmonic motion, apply it to describe the behavior of pendulums and use it to solve problems. 1. Simple Harmonic Motion: A type of motion that repeats in regular intervals of time is a periodic motion. The motion of the moon around the sun is an example of a periodic motion. Upper extreme Equilibrium position Lower extreme Amplitude Fig. 1 Vertical oscillations of a loaded spring A periodic motion has a period (T) and a frequency ( f ) . Period is the time taken for one complete motion. The time taken by the moon to go round earth once is its period. Period is represented by the letter T and its unit is second ( s ). Frequency is the number of complete motions per second. A CD that goes round 10 times a second has a frequency of 10. Frequency is represented by the letter f and its unit is s -1 which is called Hertz (Hz).
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2 Equilibrium position Left extreme Right extreme Fig.2 Oscillations of a metal strip The vertical oscillations of a spring and the oscillations of a plucked metal strip are both periodic. When the load attached to a spring is pulled down to the lower extreme, stretching the spring, the spring applies an upward restoring force. A stretched spring has potential energy. When you leave the mass, the restoring force pulls it up and all the potential energy of the stretched spring gets converted to kinetic energy by the time it is back in the equilibrium position. This kinetic energy takes the mass further up the equilibrium position to the upper extreme, thus compressing the spring. The potential energy of the compressed spring takes the mass back to the equilibrium position thus giving it kinetic energy. This process continues and the mass vibrates up and down between the upper extreme and the lower extreme as shown in fig. 1. amplitude x t 0 y Equilibrium Upper Extreme Lower Extreme Fig. 3 When the mass is at its equilibrium position, it is at x = 0. At any other position, x has a non-zero value and it is a measure of the displacement of the mass. Above the equilibrium position, the displacement is positive and
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3 below the equilibrium position, the displacement is negative. The graph on the right in fig. 3 above shows how the displacement changes with time. The maximum displacement of the mass from the equilibrium position is called the amplitude of vibration . The amplitude is denoted by A in the figure. As the displacement of the vibrating mass changes with time, it has a velocity and acceleration. The acceleration is caused by the restoring force.
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