Wahadlo o dlugosci 160 cm ma okres drgan 2,4s. Oblicz okres drgan wahadla o dlugosci 10cm Poproszę z obliczeniami

[latex]dane:\T_1 = 2,4 s\l_1 = 160 cm = 1,6 m\l_2 = 10 cm = 0,1 m\szukane:\T_2 = ?\\Rozwiazanie:\T = 2 pi sqrt{frac{l}{g}}\\T_1= 2 pi sqrt{frac{l_1}{g}}\\T_2 = 2 pi sqrt{frac{l_2}{g}}\\frac{T_1}{T_2} = frac{2 pi sqrt{frac{l_1}{g}}}{2 pi sqrt{frac{l_2}{g}}}=frac{sqrt{l_1}}{sqrt{l_2}}\\T_2cdotsqrt{l_1} = T_1cdotsqrt{l_2} /:sqrt{l_1}\\T_2 = T_1sqrt{frac{l_2}{l_1}}\\T_2 = 2,4scdotsqrt{frac{0,1m}{1,6m}} = 2,4scdotsqrt{0,0625}=2,4scdot0,25[/latex] [latex]T_2 = 0,6 s[/latex]