Problem 8.30 Challenge

จาก \(Στ = Iα\)

\(-2ky\frac{L}{2}\cos \theta =\frac{1}{12}mL^{2}\frac{d^{2}\theta}{dt^{2}}\)

\(\frac{d^{2}\theta}{dt^{2}}+\frac{6kycos\theta}{m(L/2)}= 0\)

\(\frac{d^{2}\theta}{dt^{2}}+\frac{6ksin\theta \cos \theta}{m}= 0; \sin \theta =\frac{y}{L/2}\)

\(\frac{d^{2}\theta}{dt^{2}}+\frac{6k}{m}\theta = 0; sinθ \approx θ\) และ \(cosθ \approx 1\)

จาก \(ω_{0} = \sqrt{\frac{6k}{m}}\)

\(\frac{2\pi}{T}=\sqrt{\frac{6k}{m}}\)

\(T = \pi \sqrt{\frac{2m}{3k}}\;\blacksquare\)