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1. One of the most important examples of periodic motion is simple harmonic motion (SHM), in which some physical quantity varies sinusoidally. Suppose a function of time has the form of a sine wave function, y(t) = Asin(2πt / T ) (23.1.1) where A > 0 is the amplitude (maximum value).
In this section, we examine some examples of damped harmonic motion and see how to modify the equations of motion to describe this more general case. A guitar string stops oscillating a few seconds after being plucked.
Examples: water waves, sound waves, and seismic waves. Electromagnec waves: These waves require no material medium to exist. Light waves from stars, for example, travel through the vacuum of space to reach us. All electromagneOc waves travel through a vacuum at the same speed c = 299 792 458 m/s.
Eq.(4) is the desired equation of motion for harmonic motion with air drag. It models what is known as damped harmonic oscillations, and is more realistic than the case where b is assumed to be zero. It can thus be readily applied to most every-day oscillating systems provided they can be defined one-dimensionally.
Lecture 6 - Damped harmonic motion Text: Fowles and Cassiday, Chap. 3 Simple harmonic motion is an idealization of most physical systems: in general there is some dissipative force present that robs the system of energy and reduces the amplitude of vibration. Here, we consider the damping effects of a drag force that is
I.4 Damped simple harmonic motion If there is …………. to motion then the spring / mass (or pendulum) will gradually lose …………... To model this, we have to introduce a …………… ………. into our SHM analysis. The retarding force (in this analysis) is proportional to the velocity Balancing forces; (b is a constant)
Topic 2: Damped harmonic motion Introduction So far in the discussion there is nothing in our models or equations to remove energy from the oscillations. We might imagine though that there are things that could remove energy. Examples are 1. Friction in any moving parts (including the spring) 2. Air resistance