Question

Can i please get the answer to this?

Numerical method engineering problem: steady-state configuration of mass-spring system. Assume m1 = 2 kg, m2 = 3 kg, m3 = 2.5 kg, k’s = 10 kg/s2 and use LU decomposition to solve for the displacements and generate the inverse of [K], substituting the model parameters with g = 9.81, but add a third spring between masses 1 and 2 and triple k for all springs. No need to calculate the inverse matrix. Report the three force balance equations at steady state, their matrix form, and the solution vector calculated using Excel, Matlab, Mathcad, or C++. No need to provide the code.

Answer 1

From the free-body diagram and static
equilibrium: kx = mg (g = 9.81m/s 2 ) °
k=mg/ xp = !kin = 86.164 °
The sample standard deviation in computed °
stiffness is: ! = (ki" py) 2i=1n#n"1= 0.164
Assume: x(t) = aert . Then: rt x! = are andrtxare
2u=.
Substitute into equation (1) to get: mar 2 e rt + kae
t=Omr2+k=Or=+#kmi
Thus there are two solutions: x1 = clek mi!"#$
% &t, and x2=c2e'kmi!"#S % &t
where (n = k m = 2 rad/s The sum of x1 and x2 is
also a solution so that the total solution is: it it x x x
cece222121!=+= + Substitute initial
conditions: xO = 1 mm, vO = 5 mm/s x(0) = cl + c2
= xO = 1! c2 = 1" cl, and v(O) = x (0) = 2icl " 2ic2 =
v0 =5 mm/s !"2cl + 2c2 = 5i.
Combining the two underlined expressions (2 eqs
in 2 unkowns): "2cl + 2"2c1=5i!cl=12"54i,
and c2 = 12+ 5 4i Therefore the solution is: x = 1
2154i1"#SHW&' S2it+12+54i"#5%&'e lit
Using the Euler formula to evaluate the
exponential terms yields:x =12!54i"#S$%&
‘(cos2t + isin 2t)+12+54i1"#5% &'(cos2t!
isin2t) ( x(t) = cos2t + 5 2 sin2t = 3 2 sin(2t + 0.7297)
Using Mathcad the plot is: xt cos 2.t.52sin2.t