Consider a semi-infinite string, initially level and at rest. We jiggle it up and down at...
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Consider a semi-infinite string, initially level and at rest. We jiggle it up and down at the end sinusoidally. The string vibration problem can be formulated as follows: Utt = c²uxxy 0<x<∞, t>0 u(x, 0) = u₁(x, 0) = 0, 0<x<∞ u(0, t) = sin (2πt), t>0 Solve the above problem by using the general solution u(x, t) = F(x- ct) +G(x + ct) Find the analytical expression and sketch the solution in the x-t plane for c = 1 and at time instants t = 0.5, 1.0, 1.5, and 2. Consider a semi-infinite string, initially level and at rest. We jiggle it up and down at the end sinusoidally. The string vibration problem can be formulated as follows: Utt = c²uxxy 0<x<∞, t>0 u(x, 0) = u₁(x, 0) = 0, 0<x<∞ u(0, t) = sin (2πt), t>0 Solve the above problem by using the general solution u(x, t) = F(x- ct) +G(x + ct) Find the analytical expression and sketch the solution in the x-t plane for c = 1 and at time instants t = 0.5, 1.0, 1.5, and 2.
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This problem involves the wave equation for string vibrations which is typically written as utt c2 uxx where uxt is the displacement of the string at ... View the full answer
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
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