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Week 6 Notes

by: Jonah Leary
Jonah Leary
GPA 3.284
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About this Document

Some of the things we covered in class last week.
Experimental Measurements and Instrumentation
Allen Jackson
Class Notes




Popular in Experimental Measurements and Instrumentation

Popular in Mechanical and Materials Engineering

This 2 page Class Notes was uploaded by Jonah Leary on Saturday October 8, 2016. The Class Notes belongs to ME 3600 - 01 at Wright State University taught by Allen Jackson in Fall 2016. Since its upload, it has received 57 views. For similar materials see Experimental Measurements and Instrumentation in Mechanical and Materials Engineering at Wright State University.

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Date Created: 10/08/16
ME 3600 Notes – Week 6 Chapter 8: Signals Periodic: To repeat regularly over a period of time or space y(t+T =y(t) yt)=Asin(ωt+ϕ) [rad ] A=Amplitude ω=circular frequency s ω=2πf t=time [s]Φ=phase [rad] f=frequency [Hz=1/s] 2π 1 = T=period [s]= ω f yt)=Acos (ωt)+Bsin ωt =Ccos ωt+ϕ ) C=√(A +B ) 2 ϕ=tan −1B = −ϕ A 2 A usually associated with cosine, B with sine 3.82T R8.1: y=3.8sin(ωt) , find RMS: y rms ∫ y dt T 0 A RMS= √2=2.687 2 R8.2: A is periodic T T 0→2T:y=0if 0≤t ≤ y=Aif ≤t≤T R8.7: 2 2 T 2 1 2 2 1 T 2 A2 T yrms= ∫ 0 dt+ ∫ A dt= if yt)=At from to T, T 0 T T 2 2 2 T 2 3 T 2 2 y 2= 1 ∫ A t dt= A t T= 7A T rms T T [ 3T 24 2 2 R8.9: Find cyclic frequency, period, and circular frequency of 13,000 rpm f =13000 =216.67Hz T= =0.00462s ω=2πf=1361 rad 60 f s Chapter 9: Fourier Series Even function: f(x= f (−x) Odd function: − f x = f (−x) A cos 2πnt +B sin 2πnt T n ( T n ( )T 2 ¿ A = 2 ∫ yt)dt Fourier Series: A ∞ 0 T −T yt)= 0+ ∑ ¿ 2 2 n=1 T T 2 2 A = 2 ∫ yt)cos 2πnt dt B = 2 ∫ y(tsin 2πnt dt n T −T ( )T n T −T ( )T 2 2 When y(t) is even, then B =n When y(t) is odd, then A =0n N A 2−1 A N yt)=y rδt = 0+ ∑ akcos 2πrk +b kin 2πrk + 2cos(πr) 2 k=1( ( N ( ) N 2 ) a knd b ake coefficients for Discrete Fourier Function rd R9.1: Find 3 Fourier coefficient of triangle wave where h=1 (consider to be periodic) 0 1 4 Even function so A3=∫ (t+1)cos(3πt)dt+∫ (1−t)cos(3πt)dt= 2=.045 −1 0 9π


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