In this problem we have to design a scale that can accurately weigh masses of 0.

Question

In this problem we have to design a scale that can accurately weigh masses of 0.2kg and 1.0kg with the condition that 0.1kg stretches the spring at least 1cm and that the scale reaches within 1/2 mm of equilibrium as quickly as possible (This means that the spring must be Overdamped or Critically Damped). The spring constant (k) and the Damping constant (c) are unknown or are varied to make this situation possible. How can we set this up to make the scale both accurate and critically damped using the equation:

X'' + cX' + kX = 0

Explanation / Answer

http://ww2.justanswer.com/uploads/RyanP97/2010-07-19_134205_UnderdampedMotion.pdf

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