A spring/mass/dashpot system has mass 1 kg, damping constant 7 kg/sec and spring constant 12 kg per sq sec. The system starts at rest and then has an external force of Newtons applied after seconds. The IVP below models the system:
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The Laplace transform of the IVP has solution where represents the Laplace transform of the forcing term and represents the transfer function.
The weight function is the inverse Laplace transform of the transfer function.
The solution to the IVP is the convolution of the forcing term with the weight function.
,
The Laplace transform of the IVP has solution where represents the Laplace transform of the forcing term and represents the transfer function.
The weight function is the inverse Laplace transform of the transfer function.
The solution to the IVP is the convolution of the forcing term with the weight function.