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###### In the following problems use Laplace transforms to solve for u(r) Keep mind. however. that y() and W() Mst be defined tor al over the semi-infinite dmain ( < 00 10 US the Laplace transform method. Hence appropriate moclification to the applied load W() OHL the right hatucl sicle of the abore diflerential eqquation for uls) must he performed as follows,d'u(r) f() 0 <! < 0_ dr'whire f() is the appliedl loaul delinedl over 0 < " < &-Write down f(2). 0 < x 0, if

In the following problems use Laplace transforms to solve for u(r) Keep mind. however. that y() and W() Mst be defined tor al over the semi-infinite dmain ( < 00 10 US the Laplace transform method. Hence appropriate moclification to the applied load W() OHL the right hatucl sicle of the abore diflerential eqquation for uls) must he performed as follows, d'u(r) f() 0 <! < 0_ dr' whire f() is the appliedl loaul delinedl over 0 < " < &- Write down f(2). 0 < x 0, if the bcntn is Idler constant load of Wo for 0 < r < L/2 Write dlown f(2)0 < " 0, il the ba is struck at its free cd _ = L with a impulsive force AId no other force ats tlie bcI , Find ylr) in part (b) given that y(O) = 0, v(0) 0, v"(L) =0 and 4"(L) =0.

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