SHM oscillation

子路

2010-01-13 5:50 am

in a spring-mass system, a periodic driving force is applied to it. it is known that the amplitude of the system is determined by
(1)how close the driving frequency towards the resonant frequency
(2)degree of damping

how about the amplitude of the driving force. does it affect the amplitude of the system? if yes, what is their relationship?

回答 (1)

天同

2010-01-14 4:27 am

✔ 最佳答案

Yes, the amplitude of the driving force aggects the amplitude of the oscillating system.

The differential equation that describes such oscillating system is,

m(d^2x/dt^2) + R(dx/dt) + kx = (Fo).sin(wt)
where m is the mass of the oscillating object
R is the damping constant,
k is the sprinf constant
Fo is the amplitude of the driving force
w is the angular frequency of the.driving force

By solving the defferential equation, it can be shown that the amplitude of the oscillating system, A, is given by

A = (Fo)/square-root[(k-mw^2)^2 + (wR)^2]
It is obvious that the larger the amplitude of the driving force, the larger is the amplitude of oscillation.

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