Answer :
Answer:
38.847 seconds
Explanation:
m = Mass
x = Compression of spring
k = Spring Constant
g = Acceleration due to gravity = 9.81 m/s²
[tex]F=mg[/tex]
From Hooke's law
[tex]F=kx\\\Rightarrow 0.05\times 9.81=k(11.25-10)\times 10^{-2}\\\Rightarrow k=\frac{0.05\times 9.81}{(11.25-10)\times 10^{-2}}\\\Rightarrow k=39.24\ N/m[/tex]
Additional mass
m = 0.1+0.05 = 0.15 kg
Angular frequency
[tex]\omega=\sqrt{\frac{K}{m}}\\\Rightarrow \omega=\sqrt{\frac{39.24}{0.15}}\\\Rightarrow \omega=16.17405\ rad/s[/tex]
Time for one oscillation is given by
[tex]T=\frac{2\pi}{\omega}\\\Rightarrow T=\frac{2\pi}{16.17405}\\\Rightarrow T=0.38847[/tex]
For 100 oscillations
[tex]100\times 0.38847=38.847\ s[/tex]
The time needed for hundred oscillations is 38.847 seconds