Дано:
$\frac{T_{1}}{T_{2}} = \frac{3}{2}$.
Найти:
$\frac{l_{1}}{l_{2}}$ − ?.
Решение:
$T = 2π\sqrt{\frac{l}{g}}$;
$T_{1} =\frac{3T_{2}}{2}$;
$2π\sqrt{\frac{l_{1}}{g}} = \frac{3}{2} * 2π\sqrt{\frac{l_{2}}{g}}$;
$2\sqrt{l_{1}} = 3\sqrt{l_{2}}$;
$\sqrt{\frac{l_{1}}{l_{2}}} = \frac{3}{2}$;
${\frac{l_{1}}{l_{2}}} = (\frac{3}{2})^{2} = \frac{9}{4} = 2,25$.
Ответ: в 2,25 раза.