Piet Lammertse on spring-mass systems

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Spring-mass systems

importance of the spring-mass model

The spring-mass system seems like a bit of a toy for high school physics nerds.

damped spring-mass equations

The solution for the motion of a freely oscillating ( non-driven ), damped, spring-mass system is :

x = A . e^{− a t} . cos ω t

(1)

Here ω is an angular frequency in [ rad/s ], and a is a decay factor. This can also be written as a = 1/τ, where τ is called the decay time constant. The idea is that the system oscillates with anangular frequency of ω radians per second, while the amplitude decays by a factor of 1/e per τ seconds. The derivation can be looked up in textbooks. The velocity v is the time derivative of the position x :

v = A . [− a . e^{− a t} . cos ω t - a . e^{− a t} . sin ω t]

= A . e^{− a t} . [− a . cos ω t - ω . sin ω t]

(2)

TBW.