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Enter the necessary data and click on 'Calculate' to obtain the displacement-time curve of the 1 DOF system under the specified loads.
Vibration Equations - 1 degree of freedom (DOF)

The motion of a mass with one degree of freedom (DOF) with damping is described by the following second-order differential equation:

m * x'' + c * x' + k * x = F(t)

  • m: Mass of the structure.
  • x(t): Displacement of the mass from its equilibrium position as a function of time.
  • c: Damping coefficient.
  • x'(t): Velocity of the mass displacement as a function of time.
  • k: Elastic constant (stiffness) of the system.
  • F(t): External force applied as a function of time.

Methodolody: Expand explanation imagen flecha
Calculation process
Input data
Spring stiffness
Initial amplitude:
Initial speed:
External force [[t0,F0],[t1,F1]...[tn,Fn]]:
Minimum number of seconds to plot:
  1. The force should be entered as a vector of time-force data pairs. For example, a rectangular force would be [0, 0],[2, 0],[2, 15],[8, 15],[8, 0]
  2. A null force would be [0, 0].
  3. The calculation is performed using finite differences employing the Euler method, thus employing a linear approximation of velocity and position. This entails an associated error due to precision, which is mitigated by utilizing at least 100 points per second.
Graph - Displacement and force
Other graphs
Tabulated results
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