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Day. A Roint Pluared plucked Sਦੇ ਆ guarter s Assignment #01 taught at din length shown below. and released ksom rest Determine the ensuing motion. 7 अपने 3/4 A taught stsing is initially deformed into the shape shown figure and released kom Use the travelling wave solution to determine its subsequent E rest motion. fin) **(1) Xronet) f(x-ct) fit d .
Date: Day: MTWTED Determine the fundamental Frequency qa uniform string of I length e hanging freely oun weight Pottion, loaded 12 X يصا (6) (4 possible admissible qutus for hanging string vibrations A string q length e has both ends fixed. At time t-o, its énitial shape is descrito ed wlno)= Isinan xl if os kel/ by iz fly Sue and is se leased from sest . the model sleper position method to determine its displacement at where ł is the fundamental 9 . period % the string steing. Plot thit function to show the shape string at instant t=lTo og the Baber l'aper Products
Date: problem w Day: MTWTED 2 solue utilizing the tsewelling wawa method Show diep la catent shape at t/Toro, 1/16 1/18, 1/4, 316, and , , (6 solve wave shay t 7 having particle . . o method. Shoy travelling displaced shape shape at t/ Too Gol 0.2 0.3, 0.40.5. Set up a koi for the example Frequency determinant Ostsing 27 attached en one quarter point I problem use the two displacement functions w, and wz and measure left boundary for both so that wo, and free ozredu My credo respectively. e expand the determinant and boy a thig nometric identities the resulting equation to the form of sio ß.com 38 tsin 32. /Ntoß sin p-coß , from the functions valid ما are means try to Treduce 7. 3ß - 4 u 17 unsuccessful, verify that the
a rout u it is А total two 7 out dift رطه mod d 'd are constant determinant is proloably by showing that ß2.4136 g its when it ..5 for composite stling longth I consiste segments al and bd (shown below) each having uniterm mass densitike up and de respectively, where f is here the average hell density of the entire entire string a Derive the the put frequency er for into tom containing B= wijsh .alb andeld non-dimensionales parameters, b b alb=1 and eld=5. solue the first pour first four non-dimensional - grequencies. Compare these with the ones for uniform string having the same total mass. Labok .bl. system let de l Baber Paper Products
Date: Day: MIWIES o Consider the transuerse vib q beam to write down the governing eg for the free hanegenoul material prop dstica non- cross- sedian areal as A(Z) = A (W²+1). Also write it's end conditions where end is attached to mass m and other end is attached to one spring q stiffness unit q blength attached 10 wave s 16 Determine the free vibration Frequencies and mode shapes elastic bear 우 whase both ends to dampers. ( Consider ID undanped and damped the interval {o, a hamgenous Dirichiet Boes wrot = what=0 The de dissipation I damping herm is propertional to velocity. I IL assumed that the final temperature distribedlon given by w (U,I)= F(X) It is required o initial temperature I(W) where ogs oves subject to is find profile Baber Paper l'roducts
Date: Day: MTWTFS who T (21) = Lilno) and aw (no) = 0 while solving the initial ioverse problend The general sol ter 2 egg motion. taught 7 string whose ends BU by free , is given to wrait). 2 Wn(xt) = Zusmaxle Castrent 8 Ž What) = -1 I + both are n=1 response initial displacement + Dn sin ncat T Determine the complete vibrodional when and initial velocity are taken wao) = 1 and au(xo) = 2x+1. dt use the closed solection method to evaluate the displacement bo at the middle vibrating transver absense da damping. The string is stretched to length with two fixed ands and subjeded to uniformly distributed sina soidal sina soidal forcing the string versly in the Baber Paper Products
Date: Day: MTWTER both are Corrent בול T(2) = wlno) and aw (ao) = 0 while solving the initial lover se problend. The 0 general sol taught string of g motion for whose erds by free , is given to wrut) = { Wn(at) = Zeus nax consoles Con t + Dn sin ncat 다 Determine the complete vibrodional- response when initial displacement and initial velocity are taken who) = 1 and alu(xo) = 2x+1. dt 6 use the closed solution method to evaluate the displacement at the middle vibrating thensversly in absense is stretched to length l two fixed ands and uniformly distributed sina soidal forcing the string The sthing with 122 subjected to a Baber Paper Products
Day (MDWTIES ro are constants pressure prxst)= q. sin ant whose and (10 let The eigen funcion string a length a unit whose both ne ends assumed c are free 나 X (2) - x²(x-a). оncti pension Find DE and mod k E g the the string when lo the sothing is taken as Unity . Obtais approximate pequency using Ray leigh method ( (15 let the shape a Da vibrating thing fundamental mode 4 length a hanging vestical position loadeda capproximated be weight X 2) = Cat CX². Rayleigh-Ritz method to obtain approximate prequency and 1st two mode shape Note that the tensiar section f the stering is: T= 19 (1-x) approximati in ang Baber Paper Products
Date: Day: MTWTES and are constants o pressure prxst)= q sinant whose (10 let the eigen fondin unit a whose both assumed string a length of a unit ends as: are free the as a hang in osition dadad X(21) = x²(x-a). Find mot pot and mark E g in the othing is taken string whenes tension Unity, obtain approximate prequency using Using Rayleigh methed let the fund undamental mode shape a vibrating thing vestical loaded own weight capproximated at X G) = Cat C₂X². use Rayleigh-Ritz method to n- obtain an approximate 1st two approximate mode shape Note that the tensia 007 Section f the stering is T = 29 (1-x) weight be requency and Baber Paper Products