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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 1:25 |
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Conference: Bucharest University Faculty of Physics 2005 Meeting
Section: Atmosphere and Earth Science; Environment Protection
Title:
Amplification Factors in Oscillatory Motion
Authors:
B.-F. Apostol, C. Cioflan, St. F. Balan
Affiliation:
National Institute for Earth Physics, Bucharest, Romania
E-mail
Keywords:
amplification factor,effects of seismic movements
Abstract:
The forced oscillatory motion with damping is reviewed and amplification factors are defined and computed at resonance for displacement, velocity and acceleration. The amplification for external shocks is also estimated.
We start by considering a particle of mass m and coordinate x(t) being subjected to an elastic force –kx, a friction force and an external force f(t); k denotes the elastic force constant and miu is the friction coefficient.
The amplification factor of the displacement is defined as the ratio between maximum values of the coordinate modulus (maximum values of the oscillator displacement at resonance) and maximum displacement (of the particle under the action of the external force exclusively) . It is obtained Fd=1.18, 1.96, 2.75 and 3.53 for k=1, 2, 3, 4 and corresponding for times t=(2k+1)T/4. Similar analysis holds for the velocity and the acceleration.
Amplification factors are of particular relevance in analyzing the effects of the seismic movements, as well as in modeling the mechanism of the seismic focus. Other types of amplification factors appear in wave propagation as a consequence of nonlinear elasticity.
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