Pad O MasteringPhysics: Chapter 14 Reading Review Course Home Page-201810-PH-105

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Pad O MasteringPhysics: Chapter 14 Reading Review Course Home Page-201810-PH-105-001 ? Chapter 14 Reading Review Sine and Cosine Function Behavior 1 of 16 Equation of a typical sinusoidal function in physics Motion where something oscilates regularly back and forth (also known as harmonic motion) a part of everyday life, such as boning on a tampolne. swinging on a swing, and shock absorbers on a car. All of these examples can be modeled by a mass oscllating up and down on a spring as shown in This shows a bail starting at a position y A above its equilibrium position of y0, (which s the position it would naturally hang if it was not oscilating). When the ball is released, it fals through its equilbrium position, down to-A and back up to A. The bail's round trip takes a total Sme of tT. If the ball is fairly dense and the spring is of high quality, this motion wil repeat identically for many round trips or cycles. We can graphically depict this up and down motion by plotting the vertical position of the ball as a function of time for one trip The curve in this figure is a cosine function with the formula v(t)- A cos -A where the argument is measured in radians. caled the amplitude of the wave (which is the distance rom the equilbrium position to the peak), and T is called the period of the wave (which is the time for one complete cycle). Nobice that the wave patten will repeat every time he bal has been oscilating for one period: y(t = 3T) = Acos( 2.72) = Acos(6?) = Acos(2x) ?the bal is hung on a "stiffer" spring. T wil be shorter and the wave wi. look more compact 4mearing the wave peaks wil be closer together) On the other hand, f the ball is hung on a "looser spring, T wil be longer and the wave will look more spread out (meaning the wave peaks will be tarther apart t the ball is lifted higher before being let go, A will be larger, and if it is lifted lower before being let go, A will be smaller Part A-Indentifying parts of a cosine wave Identfy A and T for the cosine function shown in y (m) Express your answer as the amplitude (in m) followed by the period (in s) separated by a comma. -2 -3

Explanation / Answer

Part A. form the given graph,

A = 3 m

T = 2 s

3, 2

Part B. amplitude is tripled, A = 9 m

preiod is cut in half, T = 1 s

hecne the fourth plot is the right one

option d)

Part C. at t = 2.7 s, from the plot of part B

y = 9cos(2*pi*t)

y = 9cos(2*pi*2.7 rad) = -2.78115294937 m

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