First slide

Simple hormonic motion

Question

A weighted glass tube floats in a liquid with len8lh /of ' the tube immersed in the liquid. It is pushed down through a certain distance y and released. The frequency of oscillations will be

Moderate

A

$2 π \sqrt{(g / l)}$
B

$\frac{1}{2 π} \sqrt{(l / g)}$
C

$\frac{1}{2 π} \sqrt{(g / l)}$
D

$\frac{1}{2 π} \sqrt{(g / y)}$

Solution

$Restoring force = A y ρg acceleraion = \frac{Ayρg}{Alρ} = \frac{gy}{l} T = 2 π \sqrt{\{y / (\frac{gy}{l})\}} or n = \frac{1}{2 π} \sqrt{(\frac{g}{l})}$

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