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Advanced Engineering Mathematics

Advanced Engineering Mathematics. LAPLACE TRANSFORM. Laplace Transform. Laplace Transform. Problem 1:. Linear Transform. Laplace Transform. Problem 2:. Evaluate L {t}. Transformation Laplace. Problem 3:. Evaluate L {e -3t }. Transformation Laplace. Problem 4:.

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Advanced Engineering Mathematics

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  1. Advanced Engineering Mathematics LAPLACE TRANSFORM

  2. Laplace Transform

  3. Laplace Transform Problem 1:

  4. Linear Transform

  5. Laplace Transform Problem 2: Evaluate L{t}

  6. Transformation Laplace Problem 3: Evaluate L{e-3t}

  7. Transformation Laplace Problem 4: Evaluate L{sin2 t}

  8. Transformation Laplace Problem 2:

  9. Inverse Transform

  10. Linear Transform

  11. Inverse Transform Problem 1:

  12. Inverse Transform Problem 2:

  13. Inverse Transform Problem 3:

  14. Axis of symmetry Deflection of curve Applications Deflection of Beams Beam is assumed as a homogeneous, and has uniform cross sections along its length Deflection curve can be derived from differential equation based on elasticity concept.

  15. L 0 x y(x) y Applications Deflection of Beams Elasticity theory: bending moment M(x) at a point x along the beam is related to the load per unit length w(x)

  16. L 0 y(x) x y(x) y Applications Deflection of Beams

  17. L 0 x y(x) y Applications Deflection of Beams • y(0) = 0 at embedded end. • y’(0) = 0 (deflection curve is tangent to the x-axis at embedded end) • y”(L) = 0, bending moment at free end is zer0. • y”’(L) = 0, shear force is zero at a free end. EIy’’’ = dM/dx is the shear force.

  18. w0 Wall L y Applications Determining deflection of a Beam using Laplace Transform x A beam of length L is embedded at both ends. In this case the deflection y(x) must satisfy:

  19. Applications Determining deflection of a Beam using Laplace Transform

  20. Applications Determining deflection of a Beam using Laplace Transform

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