Question

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

Answer 1

30.65 Kg.

Step-by-step explanation:

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

`T=2\pi\sqrt[]{(m)/(k)}`

So, solving for m, we get:

`\begin{gathered} (T)/(2\pi)=\sqrt[]{(m)/(k)} \\ (T^2)/(4\pi^2)=(m)/(k) \\ (T^2k)/(4\pi^2)=m \\ m=(T^2k)/(4\pi^2) \end{gathered}`

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

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

Then, the mass of the object is 30.65 Kg.