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A person wants to make a metronome for music practice. He uses a 27-g object attached to a spring to serve as the time standard.

a. What is the desired spring constant of the spring if the object needs to make 1.00 vibrations each second?
b. What are the assumptions that you made?

Respuesta :

cjmejiab

To solve this problem we will apply the concepts related to frequency in a spring mass system. For this purpose we will define the frequency in this type of systems as

[tex]f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}[/tex]

Here,

k = Spring constant

m = Mass

PART A) The frequency would be 1Hz[tex](1s^{-1})[/tex] and the value of the mass is [tex]27*10^{-3} kg[/tex] replacing and solving to find k we have that,

[tex]f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}[/tex]

[tex]1Hz = \frac{1}{2\pi} \sqrt{\frac{k}{27*10^{-3}}}[/tex]

[tex]k = 1.065N/m[/tex]

Therefore under that condition the esired spring constant of the spring is 1.065N/m

PART B) I assume that the spring obeys Hookes law, and ignore any possible damping due to air resistance or friction.

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