Question

3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia density p, length L, with an attached end mass, m, connected to a rigid wall via a linear spring of spring constant, k, see Figure. Let the longitudinal vibration of the bar be Wa.f). (a) [4] Write down the boundary conditions. m E, p Boundary condition at x 0 Boundary condition at x L (b) [81 Derive the equation for the natural frequency (c) 18] Assume the initial condition Wx.0) )0) and W(x.0)-0. Find the free vibration w rd). Note the initial condition implies an in s delivered at r-o to the rod a[ 0 integrals (8)dx-I for x 0. and jodor 0, and 0 for other x and / values. Note also the

Answer 1

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ATE: Boundov% Conditions al- z=0 Th d2 Musthe eq.ual to dCS っ canned wiL

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