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