Answer:
(a) 7.1 m /sec
(b) 339.9 N/m
(c) 19.91 cm
Explanation:
We have given mass m = 267 gram = 0.267 kg
Time period T = 0.176 sec
Total energy of the oscillating system = 6.74 J
We know that energy is given by
(a) [tex]Ke=\frac{1}{2}mv_{max}^2[/tex]
[tex]6.74=\frac{1}{2}\times 0.267\times v_{max}^2[/tex]
[tex]v_{max}=7.1m/sec[/tex]
(b) Now [tex]\omega =\frac{2\pi }{T}=\frac{2\times 3.14}{0.176}=35.681rad/sec[/tex]
We know that [tex]\omega =\sqrt{\frac{k}{m}}[/tex]
[tex]35.68=\sqrt{\frac{k}{0.267}}[/tex]
[tex]k=339.9N/m[/tex]
(c) We know that energy is given by
[tex]E=\frac{1}{2}KA^2[/tex]
[tex]6.74=\frac{1}{2}\times 339.9\times A^2[/tex]
[tex]A=19.91cm[/tex]
