Answered

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Determine the mass of an object when the period of oscillation is 11 s and spring constant is 10 N/m.

Sagot :

Answer:

30.65 Kg.

Explanation:

The period of oscillation T, the spring constant k, and the mass m are related by the following equation.

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

So, solving for m, we get:

[tex]\begin{gathered} \frac{T}{2\pi}=\sqrt[]{\frac{m}{k}} \\ \frac{T^2}{4\pi^2}=\frac{m}{k} \\ \frac{T^2k}{4\pi^2}=m \\ m=\frac{T^2k}{4\pi^2} \end{gathered}[/tex]

Therefore, replacing T = 11 s and k = 10 N/m, we get:

[tex]m=\frac{(11s)^2(10\text{ N/m)}}{4\pi^2}=30.65\text{ kg}[/tex]

Then, the mass of the object is 30.65 Kg.

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