Date: Mar 11, 2014 1:07 PM
Author: Shane Richardson
Subject: mass spring system
I am trying to write a program that takes inputs n, M, d, k and outputs the loaded position of the platform , x and the number of the springs that are engaged or if it's bottomed out.
k = spring constant
n = spring pairs
M = mass of loaded platform
d = difference in height of springs
The arrangement shows 11 springs: One that touches the platform and 5 pairs of springs with d meters difference in heights. When the mass, M, is supported by the platform, the platform will move through a distance x until the weight is balanced by the force of some number of springs. The number of springs that it takes to balance the weight depends on the mass being supported.
For a single spring, when g = 9.81 m/s^2: Mg = kx if x<=d
If the mass being supported requires the center spring and the first spring pair out from the center to support it, then the balance of forces gives the following:
Mg = kx + 2k(x - d) if d < x <= 2d
I need to generalize the solution to n pairs of springs, with spring pair n = 0 to mean the single center spring and then count pairs of springs out from the center. Find a formula when spring pair n is supporting the platform for the loaded position x, of the platform. That is, with nd < x <= (n +1)d.
Any help or advice would be greatly appreciated.