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)
\[x(t) = \frac{F_{0}}{k}\left[1 - e^{-\zeta\omega_{n} t}\left(\cos(\omega_{d} t) + \frac{\zeta}{\sqrt{1-\zeta^{2}}}\sin(\omega_{d} t)\right)\right]\]