8. The displacement for the transverse vibrations of a beam satisfies the differential equation Jy ==...

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8. The displacement for the transverse vibrations of a beam satisfies the differential equation Jy == = 0, dx+ with b, where E is the modulus of elasticity, I is the moment of inertia of any cross section about the x-axis, A is the area of a cross section, and is the mass per unit length. Find y(x,t) if the boundary conditions are (0,1)=0, (L,t) =0, \(0,1) = 0, xx(L,1)=0 and the initial conditions are y(x, 0) = f(x), y(x, 0) = g(x). 8. The displacement for the transverse vibrations of a beam satisfies the differential equation Jy == = 0, dx+ with b, where E is the modulus of elasticity, I is the moment of inertia of any cross section about the x-axis, A is the area of a cross section, and is the mass per unit length. Find y(x,t) if the boundary conditions are (0,1)=0, (L,t) =0, \(0,1) = 0, xx(L,1)=0 and the initial conditions are y(x, 0) = f(x), y(x, 0) = g(x).