SDOF Systems with External Excitation
Explore how single degree of freedom systems respond to different types of external forces.
System Parameters
kg
N/m
Ns/m
N
System Information
Natural Frequency: 10.00 rad/s
Damping Ratio: 0.250
Simulation
Displacement and Force vs. Time
Governing Equation
The equation of motion for a forced vibration SDOF system
\[m\\ddot{x} + c\\dot{x} + kx = F(t)\]
Step Force
Where H(t) is the Heaviside step function
\[F(t) = F_0 \\cdot H(t)\]
For underdamped systems (ζ < 1)
\[x(t) = \\frac{F_0}{k}\\left[1 - e^{-\\zeta\\omega_n t}\\left(\\cos(\\omega_d t) + \\frac{\\zeta}{\\sqrt{1-\\zeta^2}}\\sin(\\omega_d t)\\right)\\right]\]