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Describe the motion of driven, or forced, damped harmonic motion. Write the equations of motion for forced, damped harmonic motion. In the real world, oscillations seldom follow true SHM. Friction of some sort usually acts to dampen the motion so it dies away, or needs more force to continue.
What is damped harmonic motion? If we add a term representing a resistive force to the simple harmonic motion equation, the new equation describes a particle undergoing damped harmonic motion
The critically damped oscillator returns to equilibrium at X = 0 in the smallest time possible without overshooting. Critical damping is often desired, because such a system returns to equilibrium rapidly and remains at equilibrium as well.
Learn how to model and solve the equation of motion for damped harmonic oscillations, which describe systems that lose energy due to friction or drag. Find out how damping affects the amplitude, frequency and phase of the oscillations, and see applications to pendulums and springs.
Solve the differential equation for the equation of motion, x(t). Depending on the values of the damping coefficient and undamped angular frequency, the results will be one of three cases: an under damped system, an over damped system, or a critically damped system.
Adding this term to the simple harmonic oscillator equation given by Hooke's law gives the equation of motion for a viscously damped simple harmonic oscillator. m\ddot {x} + b \dot {x} + kx = 0, mx¨ + bx˙ +kx = 0, where b b is a constant sometimes called the damping constant. Solutions should be oscillations within some form of damping envelope.
When a damped oscillator is underdamped, it approaches zero faster than in the case of critical damping, but oscillates about that zero. The equation is that of an exponentially decaying sinusoid. The damping coefficient is less than the undamped resonant frequency .
