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Unformatted text preview: Chapter 13 – Vibrations and Waves This chapter covers oscillatory motion and wave propagation. Hooke’s Law The behavior of many springs approximates Hooke’s Law : F = -kx x is the amount by which the spring is stretched or compressed from its equilibrium position and F is the restoring force exerted by the spring. The negative sign means that the force is opposite to the direction of the stretch or compression. k is the force constant of the spring (N/m) and is a measure of the spring stiffness. Example : A mass, m = 500 g, is hung from the end of a spring attached to a support. In its equilibrium position, the mass stretches the spring by 5 cm. What is the force constant of the spring? k = F/x = mg/x = (0.5 kg)(9.8 m/s 2 )/(0.05 m) = 98/m Elastic Potential Energy In a previous chapter, it was shown that the potential energy associated with the stretch or compression of a Hooke’s law spring is U = ½ kx 2 In the above example, the potential energy stored in the spring is U = ½ (98/m)(0.1 m) 2 = 0.49 J Spring oscillation Assume that one end of a horizontal spring is anchored to a support and a mass is attached to the other end. The mass is pulled a distance x = A from its equilibrium position and allowed to oscillate back and forth on a frictionless surface. The position of the mass will be given as a function of time is given by ) 2 cos( ft A x π = where the frequency of oscillation is given by m k f π 2 1 = 1 The period T of oscillation is 1/f, so k m T π 2 = The oscillation of a Hooke’s law spring is called Simple Harmonic Motion (SHM)....
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- Spring '09
- 2m, 2 m, 0.5m, 7.2 m, 3.14m