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Lecture 19

MTH 108 Lecture 19: 7.5 Simple Harmonic Motion Notes

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MTH 108
Lun- Yi Tsai

MTH 108 Precalculus Mathematics II 7.5 Simple Harmonic Motion Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section. Simple Harmonic Motion What is the simple harmonic motion? The simple harmonic motion is a kind of occasional or oscillatory movement that is under a hindering power relative to the measure of relocation from a balanced or equilibrium position. Simple Harmonic Motion Formula Sine Wave Equation ▯ ▯ y (t) = A sin 2▯ (t + T) T ▯2▯ ▯ = A sin T (t) + 2▯ = A sin▯2▯(t)▯ T = y (t + T) Motion Equation y = A sin(!t) ▯ q ▯ = A sin k (t) m Velocity Equation v = A! cos(!t) Acceleration Equation 2 a = ▯! A sin(!t) = ▯! y Total Energy Equation E = E (K + P) = KE + PE 1 2 = 2kA 1 Simple Harmonic Motion Example You are given a 9-kg particle that is moving as the following function of time where the distance is measured in meters while the time’s measured in seconds: ▯ ▯ ▯ x = 5cos 1:5t +2 What are the motion’s amplitude, angular frequency, and frequency? What would be the velocity and acceleration formulas of the given particle? Amplitude x = A cos(!t + 0
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