A spring stretches by 0.0247 m when a 4.78-kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f

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05-12-2019
Physics

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A spring stretches by 0.0247 m when a 4.78-kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f

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Khoso123 Khoso123 · Answer 1 · 2019-12-09T12:45:53+01:00

This question is incomplete.So complete question is given as

I have assumed value of f=6 Hz

A spring stretches by 0.0247 m when a 4.78-kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f=6 Hz (assumed value)

Answer:

mass=4.194 kg

Explanation:

x (Spring stretches)=0.0247 m

m(mass)=4.78 kg

f=6 Hz (assumed)

mass required attached this spring=?

Solution

[tex]k=\frac{F}{x}\\ k=\frac{mg}{x}\\ k=\frac{(4.78)*(9.8)}{0.0247}\\ k=1.89*10^{3} N/m\\ m=\frac{k}{4\pi^{2}f^{2} }\\ m=\frac{1.89*10^{3}}{4\pi^{2}(6)^{2} }\\ m=4.194 kg[/tex]