Here are some useful references:

Laplace Transform Table

Partial Fractions

Bessel Functions

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Examples of the Laplace Transform as a Solution for Mechanical Shock and Vibration Problems:

Free Vibration of a Single-Degree-of-Freedom System: free.pdf

Response of a Single-degree-of-freedom System Subjected to a Unit Step Displacement: unit_step.pdf

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Base Excitation

Response of a Single-degree-of-freedom System Subjected to a Classical Pulse Base Excitation: sbase.pdf

Response of a Single-degree-of-freedom System Subjected to a Terminal Sawtooth Base Excitation: terminal_sawtooth.pdf

Response of a Single-degree-of-freedom System Subject to a Rectangular Pulse Base Excitation: sbase_rectangular.pdf

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Applied Force

Response of a Single-degree-of-freedom System Subjected to an Impulse Force: force_impulse.pdf

Response of a Single-degree-of-freedom System Subjected to a Unit Step Force: force_unit_step.pdf

Response of a Single-degree-of-freedom System Subject to a Half-Sine Applied Force: half_sine_force.pdf

Two-degree-of-freedom Subjected to a Dirac Delta Impulse: Force: two_dof_impulse_force.pdf

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See also:

Matlab Page

Structural Dynamics

Shock Response Spectrum

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– Tom Irvine

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