Doubling only the amplitude of a vibrating mass-on-a-spring system produces what effect on the system frequency? A) increases the frequency by a factor of 2 B)...
Doubling only the amplitude of a vibrating mass-on-a-spring system produces what effect on the system frequency?
A) increases the frequency by a factor of 2
B) increases the frequency by a factor of 4
C) increases the frequency by a factor of 3
D) increases the frequency by a factor of 5
E) produces no change
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Option E is correct, that is, changing the amplitude of a vibrating mass-on-a-spring system has no effect on the frequency of the system. The frequency of a mass-spring system is only related to the mass and spring constant. This is mathematically given as:
`f = 1/(2pi) sqrt(k/m)`
where, f is the frequency of the system, m is the mass of the object on spring and k is the spring constant. Thus, the frequency of the mass-spring system is not a function of its amplitude and hence changing the amplitude, will have no effect on the frequency of the mass-spring system.
Using the relation given above, the frequency of the system can be changed by changing mass or spring constant or both. For example, frequency can be doubled by reducing the mass to 25% of its original value or using a spring of 4 times the spring constant.
Hope this helps.
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