Answer:
The mass of the block is 0.025 kg
Explanation:
Mass-Spring Harmonic Motion
When a mass m is attached to a spring of constant k, they produce a simple harmonic motion which angular frequency is
[tex]\displaystyle w=\sqrt{\frac{k}{m}}[/tex]
We also know
[tex]w=2\pi f[/tex]
which means
[tex]\displaystyle \sqrt{\frac{k}{m}}=2\pi f[/tex]
Squaring
[tex]\displaystyle \frac{k}{m}=4\pi^2 f^2[/tex]
Solving for m
[tex]\displaystyle m=\frac{k}{4\pi^2 f^2}[/tex]
We have
[tex]k=10 N/m, f=10/\pi Hz[/tex]
[tex]\displaystyle m=\frac{10}{4\pi^2 \left (\frac{10}{\pi}\right )^2}[/tex]
Operating
[tex]\displaystyle m=\frac{10}{4\pi^2 \frac{100}{\pi^2}}[/tex]
Simplifying and computing
[tex]\displaystyle m=\frac{1}{40}=0.025\ kg[/tex]
The mass of the block is 0.025 kg
