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lecture21 - Ch. 10 Simple Harmonic Motion 10.1 The Spring...

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Ch. 10 Simple Harmonic Motion 10.1 The Spring Force Probably all of you have some familiarity with a spring. If you push on a spring, it pushes back. If you pull on a spring it pulls back. And the harder you push or pull on the spring, the harder the spring pushes or pulls back. If you’re careful not to pull too hard, then you will find the following to be true: x F Applied In words, the force you apply to the spring is directly proportional to the spring’s displacement (i.e. how far it stretches or compresses). e can make this proportionality an equality by multiplying the right side by a We can make this proportionality an equality by multiplying the right side by a constant: kx F Applied = he proportionality constant, is called the pring constant The proportionality constant, k , is called the spring constant . Units? [Force]/[Displacement] = [N/m]
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The spring constant is a measure of the stiffness of the spring. The larger the spring constant, k , the stiffer the spring. Forces which are proportional to the displacement, like the spring force, are called elastic forces . F Slope = k x Elastic region Inelastic region If I pull or push on a spring with force F , then Newton’s 3 rd Law tells me that the spring pushes or pulls back with an equal and opposite force. This force is called the Restoring Force . For an ideal spring the restoring force is given by: kx F = I pull on the ball with force the Hooke’s Law If I pull on the ball with force F , the spring pulls back on the ball with restoring force – F . F -F
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kx F = The minus sign in Hooke’s Law indicates that the restoring force, F , always points a direction opposite to the displacement of the spring. in a direction opposite to the displacement of the spring. When the displacement is proportional to the restoring force, but in the opposite direction, like Hooke’s Law ( F = -kx ), the motion that results is called Simple Harmonic Motion (SHM).
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This note was uploaded on 08/04/2009 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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lecture21 - Ch. 10 Simple Harmonic Motion 10.1 The Spring...

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