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 Solution:
(1) Construct a plot of p/m and r/m.
(2) The net moment of areas about tE = XE
XE = ibtE/mE - (rutE/2mE)tE/3
therefore:
(3) t2E - (6ib/ru)tE + 6mEXE/ru = 0
tE = (6ib/2ru) - (1/2)[(6ib/ru)2 - 4(6mEXE)/ru]1/2
= (3ib/ru) - (1/ru)[9i2b - 6mEruXE]1/2
(4) At maximum deflection, the velocity is zero.
Therefore,
the net area up to t = tm must equal zero.
(ib/mE) - rutE/2mE - (ru/mu)(tm - tE) =
0, the velocity at t = tm
therefore:
(5) tm = mu/ru[ru(1/mu - 1/2mE)tE + ib/mE]
Substituting for tE:
tm = [3ib/ru - (1/ru)(9i2b -
6mEruXE)1/2](1 - mu/2mE)
+ ibmu/mEru
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