Answer:
[tex]g=2.513m/s^2[/tex]
Explanation:
From the question we are told that:
Mass Taken [tex]m=100g \approx 100*10^{-3}[/tex]
Strain on Spring [tex]l_s=22.6cm \approx 22.6*10^{2}[/tex]
Distance pulled down [tex]d_d=10.9[/tex]
Time for ten oscillations take [tex]t=18.8s[/tex]
Generally the equation for angular velocity is mathematically given by
[tex]\omega=2\pi\\\omega=2\pi*\frac{10\ oscillations}{t}\\\\\omega=2\pif=2\pi*\frac{10\ oscillations}{18.8}\\Also\\\omega=\sqrt{\frac{k}{m}} \\\omega=\sqrt{\frac{k}{100*10^{-3}}}[/tex]
Therefore
[tex]{2\pi*\frac{10\ oscillations}{18.8}}=\sqrt{\frac{k}{100*10^{-3}}} \\k=\sqrt{2\pi*\frac{10\ oscillations}{18.8}}*100*10^{-3}\\k=1.112N/m[/tex]
Generally the equation for Acceleration due to gravity is mathematically given by
[tex]F=mg\\mg=k l_s\\g=\frac{k l_s}{m}\\g=\frac{1.112*2.6*10^{2}}{100*10^{-3}}[/tex]
[tex]g=2.513m/s^2[/tex]
