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As an example, for water waves, v w is the speed of a surface wave; for sound, v w is the speed of sound; and for visible light, v w is the speed of light. The amplitude X is completely independent of the speed of propagation v w and depends only on the amount of energy in the wave.
The speed (or sometimes you might see it called velocity) of a wave (\(v\)) is how far the wave travels in a certain time. Wave speed is measured in metres per second (\(m\,s^{-1}\)).
- Period and Frequency in Oscillations. In the absence of friction, the time to complete one oscillation remains constant and is called the period (T). Its units are usually seconds, but may be any convenient unit of time.
- Characteristics of Simple Harmonic Motion. A very common type of periodic motion is called simple harmonic motion (SHM). A system that oscillates with SHM is called a simple harmonic oscillator.
- Equations of SHM. Consider a block attached to a spring on a frictionless table (Figure 15.4). The equilibrium position (the position where the spring is neither stretched nor compressed) is marked as x=0x=0.
- Summary of Equations of Motion for SHM. In summary, the oscillatory motion of a block on a spring can be modeled with the following equations of motion
When oscillations are lightly damped, the amplitude does not decrease linearly. It decays exponentially with time; When a lightly damped oscillator is displaced from the equilibrium, it will oscillate with gradually decreasing amplitude. For example, a swinging pendulum decreasing in amplitude until it comes to a stop
Where A is the amplitude of oscillation, ω is angular speed, x is displacement from the equilibrium position, v is the velocity and a is the acceleration. 13.183 - Calculating the time period
- 475KB
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Many systems are underdamped, and oscillate while the amplitude decreases exponentially, such as the mass oscillating on a spring. The damping may be quite small, but eventually the mass comes to rest. If the damping constant is b = √4mk, the system is said to be critically damped, as in curve (b).
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Figure 5.39 An object attached to a spring sliding on a frictionless surface is a simple harmonic oscillator. When displaced from equilibrium, the object performs simple harmonic motion that has an amplitude X and a period T. The object’s maximum speed occurs as it passes through equilibrium. The stiffer the spring is, the smaller the period T.
