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determine the natural frequencies of a uniform beam of iength i clamped at one end and pinned at the other endthe
problema uniform be am of length land weight wb is c1amped at one end and carries a concentrated weight wo at the other
the stiffness matrix for the system shown in figure is given asdetermine the choleski decomposition u and u-1the
using matrix iteration determine the natural frequencies and mode shapes of the torsion al system of figurethe response
in figure four masses are strung along strings of equal lengths assuming the tension to be constant determine the
given the mass and stiffness matricesdetermine the natural frequencies and mode shapes using the standard form and the
find the velocity of longitudinal waves along a thin steel bar the modulus of elasticity and mass per unit volume of
shown in figure is a flexible cable supported at the upper end and free to oscillate under the influence of gravity
repeat example by decomposing the stiffness matrix and compare the results with those given in the exampleexamplewhen
for the system shown in figure write the equation of motion and convert to the standard formthe response must be typed
find the wave velocity along a rope whose mass is 0372 kgm when stretched to a tension of 444 nthe response must be
derive the equation for the natural frequencies of a uniform cord of length i fixed at the two ends the cord is
a cord of length land mass per unit length p is under tension t with the left end fixed and the right end attached to a
a harmonic vibration has an amplitude that varies as a cosine function along the x-direction such thatya cos kx sin
write the equations of motion for the 3-dof system shown in figure in terms of the stiffness matrix by lettingm1m2m3m
the frame of prob 7-20 is loaded by springs and masses as shown in fig p7-21 determine the equations of motion and the
using area moment and superposition determine m1 and r2 for the beam shown in figure letnbsp el12el2the response must
with loads m and j placed as shown in figure set up the equations of motionthe response must be typed single spaced
determine the equation of motion for the system shown in figure and show that its characteristic equation is for equal
using the eigenvalues of problem demonstrate the gauss elimination methodproblemdetermine the equation of motion for
for the extension of the double pendulum to the dynamic problem the actual algebra can become long and tediousinstead
for the system in section the eigenvector for the first mode was determined by the gauss elimination method complete
in the method of cofactors app c4 the cofactors of the horizontal row and not of the column must be used explain whythe
draw a few other diagrams of systems equivalent to figure and determine the eigenvalues and eigenvectors for ki and mi
determine the influence coefficients for the three-mass system of figure and calculate the principal modes by matrix