Damped Harmonic Motion

Damped Harmonic Motion - Damped Harmonic Motion In most...

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Damped Harmonic Motion In most real physical situations, an oscillation cannot go on indefinitely. Forces such as friction and air resistance eventually dissipate energy and decrease both the speed and amplitude of oscillation until the system is at rest at its equilibrium point. The most common dissipative force encountered is a damping force, which is proportional to the velocity of the object, and always acts in a direction opposite the velocity. In the case of the pendulum, air resistance always works against the motion of the pendulum, counteracting the gravitational force, shown below. Figure %: A pendulum subject to air resistance of magnitude bv , where b is a positive constant. We denote the force as F d , and relate it to the velocity of the object: F d = - bv , where b is a positive constant of proportionality, dependent on the system. Recall that we generated the differential equation for simple harmonic motion using Newton's Second Law : - kx = m
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Damped Harmonic Motion - Damped Harmonic Motion In most...

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