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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.
- 16.7: Damped Harmonic Motion
This worked example illustrates how to apply problem-solving...
- 16.7: Damped Harmonic Motion
This worked example illustrates how to apply problem-solving strategies to situations that integrate the different concepts you have learned. The first step is to identify the physical principles involved in the problem. The second step is to solve for the unknowns using familiar problem-solving strategies.
For example, if this system had a damping force 20 times greater, it would only move 0.0484 m toward the equilibrium position from its original 0.100-m position. This worked example illustrates how to apply problem-solving strategies to situations that integrate the different concepts you have learned.
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.
Examples of damped harmonic oscillators include any real oscillatory system like a yo-yo, clock pendulum, or guitar string: after starting the yo-yo, clock, or guitar string vibrating, the vibration slows down and stops over time, corresponding to the decay of sound volume or amplitude in general.
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.
Example 1. Damping an Oscillatory Motion: Friction on an Object Connected to a Spring. Damping oscillatory motion is important in many systems, and the ability to control the damping is even more so.
