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Home Energy Viscous Friction and Spring  
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Viscous Friction and Spring
S = coefficient of stiffness of the spring in newtons per m then
where dx/dt is the velocity v with which the spring is extended, hence
The power is expressed by
The power expressed by the term R_{F}v^{2} is converted into heat and the power expressed by the term Svx is the power that stores energy in the spring. The energy in this system is obtained by taking the time integral of Eq. 143 as follows
If x = 0 when t = 0 there results
NOTE: dx = v dt The stored energy is Sx^{2}/2 and the converted energy is
To determine the relationship between the stored energy and that converted into heat, consider the total energy input for a final extension of the spring to a value X, then
However, the final value of x, namely X, is determined from the relationship
and
A comparison of Eq. 148 with 146 shows that the energy converted into heat is exactly equal to the energy stored in the spring, in that
This means that when a constant force is applied to such a system, it is capable of storing only onehalf the applied energy. This is true regardless of the value of the friction constant R_{F}. If the parameter R_{F} is made low, the velocity v goes up correspondingly in such a manner that the frictional energy loss remains constant. A similar situation exists for an electrical RC circuit.


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