Motion can be back and forth {vibration, motion}| {oscillation}.
period
Vibrations take time to complete one vibration.
frequency
Vibrations have number of vibrations per time unit. Period T relates to frequency f: f = 1/T.
wavelength
Moving vibration travels distance during one period.
velocity
Movement velocity v equals wavelength l times frequency f: v = l*f. Vibration velocity maximizes at center. Vibration velocity is zero at maximum displacement.
acceleration
Acceleration is zero at center. Acceleration maximizes at maximum displacement.
displacement
During vibration, object is at distance from equilibrium or center point. Amplitude is maximum displacement. Period does not depend on amplitude. Large amplitudes have large acceleration, and small amplitudes have small acceleration, so period stays the same.
phase
Two vibrations can have same angle for same displacement {in phase} or not {out of phase}.
rotations
Vibrations are similar to rotations but are back and forth, instead of around axis. Rotation looks like vibration if viewed from orbital plane.
trigonometric function
Sine or cosine functions can model vibration. Sines and cosines have varying displacement, which has maximum amplitude. Sines and cosines have varying phase angle. Angle A equals frequency f times time t times 360 degrees expressed in radians 2*pi: A = 2 * pi * f * t. If time is zero, angle is zero. If time is period, angle is zero. If time is half period, angle is 180 degrees, and sine is zero. If time is one-quarter period, angle is 90 degrees, and sine is one. Sine equals zero if angle is zero. Sine maximizes if angle is 90 degrees.
Angle A equals displacement x divided by wavelength l times 360 degrees expressed in radians 2*pi: A = 2 * pi * x / l. If displacement is zero, angle is zero. If displacement is wavelength, angle is zero. If displacement is half wavelength, angle is 180 degrees, and sine is zero. If displacement is one-quarter wavelength, angle is 90 degrees, and sine is one.
Displacement x equals amplitude A times sine: x = A * sin(2 * pi * f * t) or A * sin(2 * pi * x / l). Vibrations can shift angle: x = A * sin(2 * pi * f * t + Ao), where Ao is starting angle.
string vibration
Vibrating strings are stationary waves and have partial differential equations. Second partial derivative of function y with respect to time t equals constant (a^2) times second partial derivative of function y with respect to distance x. (D^2)y / Dt = (a^2) * (D^2)y / Dx, where (D^2) is second partial derivative, D is partial derivative, a is constant, t is time, x is distance, and y is function of time and distance. To be dimensionless, constant a equals period T in seconds divided by seconds: a = T / second. Because endpoints are stationary, function y at x = zero equals zero: y(t,0) = 0. Function y at x = one wavelength equals zero: y(t,1) = 0. For stationary waves, partial derivative of y with respect to time t, at t equals zero, equals zero: Dy(0,x) / Dt = 0. Function y at t = zero equals function of x: y(0,x) = f(x), which is odd and periodic.
Physical Sciences>Physics>Kinetics>Motion Types>Vibration
5-Physics-Kinetics-Motion Types-Vibration
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224