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Data Processing Assignment

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Added on  2020-05-03

Data Processing Assignment

   Added on 2020-05-03

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Project 1Data processing and analysis:Note; ωn = √1LCWhile; ζ = 12R√CLThen, ω2−ω1ωn=2ζ ̈V0 + 2ζωn ̇v0+ v0ωn2 = 2ζωn ̇vn ̈V0 =1δt2[v0i+2 -2v0i+1 + v0i] = 1δt[v0i+1 - v0i]δt = 1FsHence, ωn = 2πfnTherefore; ωn *δt = 2πfnfnv0i+2 = v0i+1(2-2ζ*2πfnfn) – vo0(1-2ζ*2πfnfn + (2πfnfn)2 + 2ζ(2πfnfn)(Vni+1 – Vni)where; i= 0→N−1a)Use Fourier Transforms to estimate the natural frequency of the system and its damping factor. Mx + cx + kx = fsinωt....................................(1)From the calculation below1
Data Processing Assignment_1
The value of ζ = 0.79995While ω = 0.873Lets take the passanger vehicle has a weight of; f = 10000 NWhile x(0) = 0.064 and x(0) = 0The above equation is similar to the unforced system except that it has a forcing function.To solve this equation we have to reduce it into first order differential equationLet x = v ....................(2)but v = [(f/m)sinωt – (c/m)v – (k/m)x] ..........(3)the second order differential equation has been reduced to the first order differential equationtherefore; x = y(1)x = v = y(2)equation (2) and (3) then reduced to y(1) = y(2)y(2) = [(f/m)sin(ωt) + (-c/m)*y(2) – (k/m)*y(1)]to calculate for the value of c we compaire equation (1) with the following generalized equation x + 2ζωn + ωn2 = fsinωtequating the coefficient c/m = 2ζωnωn2 = k/mfrom the calculation below ωd = 0.873 rad/sec2
Data Processing Assignment_2
ωn = 0.874 rad/secζ = 0.03328damped time period Td = 2π/ωd = 7.2 sec for 5 time cycle the interval should be 36 sec, since the plot should indicate both the transient and steady state responses, the time interval will be increasedfunction yp = forced(t,y) yp = (y(2);(((f/m)*sin(ωn*t))-((c/m*y(2))-(k/m)*y(1))));The following code represent the main codespan = (0 5);y0=(0.064;0);(t,y)=ode45(forced,tspan,y0);Plot(t,y(:,1));grid onxlabel(time)ylabel(Displacement)title(Displacement vs time)hold ontspan represent the time interval and y0 represent the initial condition for y(1) and y(2), which in turn represent the displacement x and the first derivative f x3
Data Processing Assignment_3

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