exam 1 solution me340 sp17.pdf

# exam 1 solution me340 sp17.pdf - K W Jame ~ff Exam 1 ME 340...

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Unformatted text preview: K ‘W , Jame: ﬁ~§f£§§f§ﬂﬂ Exam 1 ME 340 SP 17 (1) Given the amplitude spectrum at the right, please write down the signal y(t) which resulted in the given spectrum. Using the signal (or the spectrum), what is the long term time average of the signal? .m-H . Using the signal (or the spectrum), what is the long term time average RMS (RMS here means RMS = y(t)2 ) ofthe signal? Name: (2) As part of an experiment into the behavior of an automobile suspension an intern is asked to sample an accelerometer output for 15 seconds with a sampling frequency of 5 hz. How many total samples IV does the intern take? KV“/S’x5‘£75’ N3 THC 6R gtw'Fzse What is the time between samples? 51:: Ag -: /S— :2 ()1 sec; The intern performs an FFT with the data collected What Is the frequency increment between thew WW 3?: Vast: E'i/le: 52325:: As He Kaééce). What is the highest frequency in the FFT? £44k) Fig; 257/? ere/w/V I ”W“ 0%”; 2:43 He It turns out that there is some important dynamics which are occurring at 10 hz. What sampling frequency would the intern need to use to capture the 10 hz frequency in the FFT? £3,220 He Using this sampling frequency, if the intern wished to have the distance between frequencies in the“ \ spectrum (5f) be 0.01 Hz, how many data points, N, would need to be collected? EHM I :50‘H22: Qwé M1120 We )0 * f; (id in Name: (3) A sensor mounted to a cantilever beam indicates beam motion with time. When the beam is deflected and released (step test), the sensor signai indicates that the beam oscillates as an underdamped second order system with a ringing frequency of 10 rad/sec. The maximum displacement amplitudes are measured at three different times corresponding to the 1“, 16th and 32"d cycles and found to be 17, 9 and 5 mV. Estimate the damping ratio and the natural frequency. a: a)” st’z «:10 mil/s 77:: (1::1‘) 72c 1" T ”T figs its a man My; 5-: --,~';.xe«e>-=‘o<+24 '" of 2' : ream :ﬁaé?3’ 41% 6 Twp“? 2 Vii—‘6 ‘EMe‘gEs LO W 7' *9 me If the measurements are to have a maximum error or +/— 3 dB, what is the measurement bandwidth which this sensor/beam combination can be used? (hint: for the value of damping you calculated, will the +3dB line be reached before the —3 dB line?) H M Mfuﬁ: m MKBJ]: ‘___/_____._ 2:!th Name: Sketch the frequency response, M(m) ofthis sensor/ beam combination? (give both the magnitude and the phase angle). g" ' £313,3ng #3 What IS the peak value of the frequency response, M(o) AWF‘W “gm?“ §3%Q J Mme: ﬂég‘: \$71 gﬁmaﬁm % W/ngﬁ: | lmgga j ;Lg Tr‘149 ng {\$9.3}: i3 .' {W 2333 Using the half power method, estimate the width of the frequency response where the amplitude of the response is 0.707 of the peak value. as§£ 465%}me Oalfl’iﬁ Name: (4) Determine whether the following systems are first order or second order systems F rst order a r second order? Name: (5) in fitting the response of a first order system to a step function input, the following data taken of the response. The response function for a first order system is given as: T = F = exp(— g). in 0"" oo 1 order to find I, the equation was rearranged to the form: 111(F) : "- Z; * t, regression was applied to the data in this form (y = 3nd“), and x=t), and the output given below was presented by the statistical analysis program. II T.—Tm [III-IIIIIII l-MMMMW-Imml E: II ImmmmIIMMI IMMMWIIWWI IWEWW-Imml aImmmmmIImml I-WWHMW-IEWI _ _ X Variable 1 Line Fit Plot SUMMARY OUTPUT . 0 1 2 7 3 4 Regression Statistics { l T N l 0 Multiple R - 0998449355 ”11% 2 3 4' 0-5 Q Y RSquare 0396901135; NM __ _1 , Adjusted RSquare . 0995281353 “KW 45 wmrPredictedY Standard Error ; 0.032768066' Observations ' 7 _ XVariable 1 " '2 'ANOVA ; __ df \$5 ' MS F Significance F 1 Regression __ 1 1. 727114443 1 7271143 1608.494205- 1.81705E-07; Residual 52 0005368731 0.001074 .TotaE 6? 1. 732483174 ' . Coefﬁcients iStariclnrci Error _ tStat I P-vaiue I Lower95% ; Upper95% intercept -0.042759533; 0022327573. «191554; 0113576489 010016464. 0014525578 XVariabiel 41496719875? 0012385165E 40.106 1.81705E-07- 4152855696 —0.464882795 The equation given by the regression analysis program is: y = c0 + c1 * x. Using the output given above, what are these coefficients, co and C1? _ , C=ﬁwﬁ D C[ .7: #991974 Name: in En terms of x and y, what are/Wand t? What is the value Of’l: found by the regression anaiysis program? m. f ,. 2’: /c¢- A Z, (9! 3 The output gives the 95% confidence interval for Co and c1. Using these vaiues, give a 95% confidence interval for I: ﬂed/i < lg. < ﬁrs-2% 76 (My 4? A 2J5? The hypothesis used in deriving the equation: 11101) = m E * t , is that CO is zero. Using the output, is this hypothesis true? is _, . M limo \Q Norma! Q4}! Plot The q—q plot for the residuals ofthe fit is given in the figure below. The hypothesis in creating the fit is that the distribution of the residuals is Gaussian (normal). Does this plot indicate the residuals follow a normal distribution? Why 0 or why not? 0.04 0 I12 <9 ”A Es;- 35 i it Etieorelical Quantiles ...
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