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The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. This model is well-suited for modelling object with complex material properties such as nonlinearity and viscoelasticity .
A mass suspended from a spring, for example, might, if pulled and released, bounce up and down. On each bounce, the system tends to return to its equilibrium position, but overshoots it. Sometimes losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero or attenuate. The damping ratio ...
The graph shows the effect of a tuned mass damper on a simple spring–mass–damper system, excited by vibrations with an amplitude of one unit of force applied to the main mass, m 1. An important measure of performance is the ratio of the force on the motor mounts to the force vibrating the motor, F 0 / F 1 . This assumes that the ...
In a real spring–mass system, the spring has a non-negligible mass. Since not all of the spring's length moves at the same velocity v {\displaystyle v} as the suspended mass M {\displaystyle M} (for example the point completely opposed to the mass M {\displaystyle M} , at the other end of the spring, is not moving at all), its kinetic energy ...
A simple mass–spring–damper system, and its equivalent bond-graph form. A bond graph is a graphical representation of a physical dynamic system.It allows the conversion of the system into a state-space representation.
Another technique used to increase isolation is to use an isolated subframe. This splits the system with an additional mass/spring/damper system. This doubles the high frequency attenuation rolloff, at the cost of introducing additional low frequency modes which may cause the low frequency behaviour to deteriorate. This is commonly used in the ...
For example, calculating the FRF for a mass–spring–damper system with a mass of 1 kg, spring stiffness of 1.93 N/mm and a damping ratio of 0.1. The values of the spring and mass give a natural frequency of 7 Hz for this specific system. Applying the 1 Hz square wave from earlier allows the calculation of the predicted vibration of the mass.
For a single damped mass-spring system, the Q factor represents the effect of simplified viscous damping or drag, where the damping force or drag force is proportional to velocity. The formula for the Q factor is: Q = M k D , {\displaystyle Q={\frac {\sqrt {Mk}}{D}},\,} where M is the mass, k is the spring constant, and D is the damping ...