MCPCalc

Laplace Transform Calculator

Compute forward and inverse Laplace transforms for common canonical signal families.

Scratchpad (not saved)

What This Calculator Does

Compute forward and inverse Laplace transforms for common canonical signal families.

It combines Mode, Function Family, Polynomial Order n, a (exponential rate) to estimate Forward Transform, Sample Evaluation, Step.

Formula & Method

Core equations: \mathcal{L}\{t^n\}=\frac{n!}{s^{n+1}},\;\mathcal{L}\{e^{at}\}=\frac{1}{s-a},\;\mathcal{L}\{\sin(bt)\}=\frac{b}{s^2+b^2},\;\mathcal{L}\{\cos(bt)\}=\frac{s}{s^2+b^2}.

Notation used in the formulas: R = Forward Transform; x_{1} = Mode; x_{2} = Function Family; x_{3} = Polynomial Order n; x_{4} = a (exponential rate); x_{5} = b (angular frequency); x_{6} = c (shift).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Inputs Used

  • Mode: Used directly in the calculation.
  • Function Family: Used directly in the calculation.
  • Polynomial Order n: Used directly in the calculation.
  • a (exponential rate): Used directly in the calculation.
  • b (angular frequency): Used directly in the calculation.
  • c (shift): Used directly in the calculation.
  • Evaluate at real s: Used directly in the calculation.
  • Evaluate inverse at t: Used directly in the calculation.

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