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Unformatted text preview: (c) that the motion is not aected of the force of gravity. First, say that we have a mass m attached to a spring with constant k . Assume that the mass is under the inuence of an external force F ( t ). Denote u = u ( t ) as the position of the mass at time t . Equilibrium is seen to be at u = 0, so this also denotes the displacement from equilibrium of the mass at time t . Hookes Law states that the restoring force of the spring on the mass is F s = k u. Newtons Second Law of Motion states that F = m a is the sum of the forces on the mass: m d 2 u dt 2 = k u + F ( t ) . This can be expressed as a system of rst order dierential equations. Indeed, if we denote x 1 = u x 2 = u = x 1 = x 2 m x 2 = k x 1 + F ( t )...
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue UniversityWest Lafayette.
 Spring '09
 EdrayGoins
 Linear Systems

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