Applying Newton's Laws of Motion
As a simple example, consider a mass driven along a frictionless surface by an ideal spring , as shown in Fig.B.2. Assume that the mass position corresponds to the spring at rest, i.e., not stretched or compressed. The force necessary to compress the spring by a distance is given by Hooke's law (§B.1.3):
where we have defined as the initial displacement of the mass along . This is a differential equation whose solution gives the equation of motion of the mass-spring junction for all time:B.7
where denotes the frequency of oscillation in radians per second. More generally, the complete space of solutions to Eq.(B.4), corresponding to all possible initial displacements and initial velocities , is the set of all sinusoidal oscillations at frequency :
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Hooke's Law