massespringdamper
Massespringdamper, or mass–spring–damper system, is a simple mechanical model used to study linear vibratory motion. It comprises a rigid mass m connected to a spring with stiffness k and a damper with damping coefficient c. An external force F(t) acts on the mass. For a single degree of freedom, the equation of motion is m x''(t) + c x'(t) + k x(t) = F(t). In the absence of forcing, the homogeneous equation governs the transient response.
Key characteristics include the natural frequency omega_n = sqrt(k/m) and the damping ratio zeta = c / (2 sqrt(k
Steady-state and dynamic responses can be analyzed via the transfer function X(s)/F(s) = 1/(m s^2 + c s
Applications of the massespringdamper model include vibration isolation, vehicle suspensions, structural and mechanical vibration analysis, and