Transmissibility
Explore how forces and motions are transmitted through vibrating systems.
System Parameters
kg
N/m
Ns/m
rad/s
N
System Information
Natural Frequency: 10.00 rad/s
Damping Ratio: 0.250
Frequency Ratio: 0.500
Transmissibility Ratio: 1.000
Key Frequency Ratios
Force Transmissibility Simulation
Transmissibility Curve
Governing Equation
Equation of motion for force or motion transmissibility
\[m\\ddot{x} + c\\dot{x} + kx = F(t) \\text{ or } m\\ddot{x} + c(\\dot{x} - \\dot{y}) + k(x - y) = 0\]
Force Transmissibility
Ratio of transmitted force to input force
\[TR = \\left|\\frac{F_T}{F_0}\\right| = \\frac{\\sqrt{1 + (2\\zeta r)^2}}{\\sqrt{(1-r^2)^2 + (2\\zeta r)^2}}\]
Force isolation occurs when frequency ratio exceeds √2
\[\\text{For } r > \\sqrt{2}, TR < 1 \\text{ (isolation region)}\]