# 4_5notes - Math 114 4.5 Simple Harmonic Motion Section 001...

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Math 114 4.5 Simple Harmonic Motion Section 001 A. Simple Harmonic Motion The motion of radio waves, television waves, light waves, and sound waves all can be described by simple harmonic motion. An object that moves on a coordinate axis so that the distance d from its rest position (equilibrium) at time t is given by either ) cos( t a d ϖ = or ) sin( t a d ϖ = where a and 0 ϖ are constants, moves with simple harmonic motion. The motion has amplitude a and period ϖ π 2 . The frequency, the number of oscillations per unit time, is π ϖ 2 = f . B. Finding an Equation for an object in Simple Harmonic Motion. * Use ) cos( t a d ϖ = if the object’s motion does not begin at its point of equilibrium. * Use ) sin( t a d ϖ = if the object’s motion begins at its point of equilibrium. This avoids the need of a phase shift. ASSUME THE POSITIVE MOTION IS UPWARD. An object attached to a coiled spring is pulled down a distance a from its rest position then released. Write an equation that represents the displacement of the object from its rest position

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Unformatted text preview: after t seconds. 1. a = 10 cm T = 3 seconds An object attached to a coiled spring is pushed upward a distance a from its rest position then released. Write an equation that represents the displacement of the object from its rest position after t seconds. 2. a = 6 m 5 = f Hz 3. A tuba player plays the note E and sustains the sound for some time. Find the simple harmonic equation that represents the sound wave given that the amplitude is 0.2 and the period is 1/40 second. C. Analyzing the Motion of an Object Given that the displacement, d , in meters of an object at time t (in seconds) satisfies the given equation, A) What is the maximum displacement from its resting position? B) What is the time required for one oscillation? C) What is the frequency? 1. t d 3 sin 2 = 2. t d 2 1 cos 3 =...
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• Spring '08
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