Answer:
1)m=89.01 g
2)V(max) = 97.3 cm/s
Explanation:
Given that
K= 15 N/m
The maximum amplitude ,A=7.5 cm = 0.075 m
Given that 31 oscillations in 15 seconds ,this means that frequency f
f=\dfrac{31}{15}
f=2.066 Hz
lets take mass of the ball = m kg
[tex]f=\dfrac{1}{2\pi}\times \sqrt{\dfrac{K}{m}}[/tex]
[tex]m=\dfrac{1}{4\times \pi^2}\times{\dfrac{K}{f^2}}[/tex]
[tex]m=\dfrac{1}{4\times \pi^2}\times{\dfrac{15}{2.066^2}}[/tex]
m=0.08901 kg
m=89.01 g
The maximum speed
V(max)= ω x A
ω = 2π f= 2 x π x 2.066 = 12.98 rad/s
V(max) = 12.98 x 0.075 =0.973 m/s
V(max) = 97.3 cm/s
