F = - 2x + 1
F = -2 \((x - \frac{1}{2})\)
F = \(-2 \times 10^{-5} \times 10^{-2}(x - \frac{1}{2})\)
F = \(-2 \times 10^{-7}(x - \frac{1}{2})\)
F = - kx
k = \(2 \times 10^{-7}\)
We know that
\(\omega = \sqrt{\frac{k}{m}}\)
\(\omega = \sqrt{\frac{2 \times 10^{-7} \times 1000}{0.008}}\)
\(\omega = \sqrt{0.25 \times 10^{-4}}\)
\(\omega = 0.5 \times 10^{-2}\) rad/sec
(i) Mean position zero.
(ii) Time period \(T = \frac{2\pi}{\omega}\)
\(=\frac{2\pi}{0.5 \times 10^{-2}}\)
\(T = \frac{20\pi \times 10^2}{5}\)
\(T = 4\pi \times 10^2 \, sec\)