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![]() This shows that force, F, is proportional to the position of a mass, x times the stiffness, k of an attached spring. The value k is known as the spring constant.
Now consider Newton's second law of motion ![]() This states that force is equal to mass, m, times acceleration,a. All looks good from here.
If we equate the two, we get ![]() Which can be rewritten as ![]() Since Vibe solves ordinary differential equations (ODEs) directly, this is where we stop. However, there is a geometric solution for this ODE which is worth noting: ![]() where ![]() The derivation of this solution is left as an exercise for the reader. This mass spring simulation is not terribly interesting in its own right. What might be useful is to play with the spring stiffness k and the mass m and note that they are (inversely) related proportionally to each other. That is, increasing the spring stiffness by a factor of x causes exactly the same change in the system as does decreasing the mass by a factor of 1/x. If this isn't intuitively clear, look closely where k and m fit into the last equation above. |
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Vibe Oscillator Simulator © 2000-2003 Douglas S. Eck. Back to the Vibe Home Page § Back to Douglas Eck's Home Page Thu Jul 24 09:12:34 EDT 2003 |