Unformatted text preview: (c) that the motion is not a±ected 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 in²uence 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 . Hooke’s Law states that the restoring force of the spring on the mass is F s = − k u. Newton’s 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 ³rst order di±erential 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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 Spring '09
 EdrayGoins
 Linear Systems, Force, Friction, Mass, Uniqueness Theorem

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