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The simplest type of oscillations are related to systems that can be described by Hooke’s law, F = −kx, where F is the restoring force, x is the displacement from equilibrium or deformation, and k is the force constant of the system.
The simplest type of oscillations are related to systems that can be described by Hooke’s law, F = −kx, where F is the restoring force, x is the displacement from equilibrium or deformation, and k is the force constant of the system.
We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency. Let’s try one example of each. A medical imaging device produces ultrasound by oscillating with a period of 0.400 µs.
m + k x(t) = 0 dt2. This is the equation of motion of the mass attached to a spring. The movement is an oscillation of the mass around the equilibrium position. The equation of motion is a second order differential equation in time.
These conditions can be shown through the equation: a = − ω2 x. Where a is acceleration, ω is angular speed, x is displacement from the equilibrium position. An example of a simple harmonic oscillator is the simple pendulum, as shown in the diagram on the right. The pendulum oscillates around a central midpoint known as the equilibrium position.
Lecture 1: Mathematical Modeling and Physics (PDF) Lectures 2–3: Simple Harmonic Oscillator, Classical Pendulum, and General Oscillations (PDF) Lecture 4: Damped Oscillations (PDF)
17 Ιουλ 2018 · Emphasizing physics over mathematics, this popular, classroom-tested text helps advanced undergraduates acquire a sound physical understanding of wave phenomena.
