A spring with spring constant 18 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.5 cm and released. The ball makes 19 oscillations in 18 s seconds.

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Answer with Explanation:

We are given that

Spring constant=k=18 N/m

Amplitude,A=6.5 cm=[tex]6.5\times 10^{-2}m[/tex]

1m=100 cm

Number of oscillations=N=19

Time=t=18 s

Frequency=Number of oscillations per second=[tex]\nu=\frac{19}{18}=1.06 Hz[/tex]

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

[tex]\nu^2=\frac{1}{4\pi^2}\times \frac{k}{m}[/tex]

[tex]m=\frac{k}{4\pi^2\nu^2}=\frac{18}{4\times (3.14)^2\times (1.06)^2}=0.41 kg[/tex]

1kg=1000g

[tex]m=0.41 \times 1000=410 g[/tex]

Mass of the ball=410 g

Maximum speed of the ball=[tex]A\omega=A(2\pi\nu}[/tex])

Maximum speed of the ball=[tex]v_{max}=6.5\times 10^{-2}\times 2\times 3.14\times 1.06=0.43m/s[/tex]

Hence, the maximum speed of the ball=0.43 m/s

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