The figure shows a top-view of a rod, of length L=50cm and mass m=3kg, Undergoin

Question

The figure shows a top-view of a rod, of length L=50cm and mass m=3kg, Undergoing small oscillations in horizontal plane XY. The axis of rotation (the Z-axis) passes through the center of the bar.

A spring, of spring-constant k= 1N/m, is connected horizontally between one end of the rod and a fixed wall. When the rod is in equillibitium, it is parallel to the wall. Calculate the period of the oscillations that result when the rod is rotated slightly and released

The figure shows a top-view of a rod, of length L = 50cm and mass m = 3kg, Undergoing small oscillations in horizontal plane XY. The axis of rotation (the Z-axis) passes through the center of the bar. A spring, of spring-constant k = 1N/m, is connected horizontally between one end of the rod and a fixed wall. When the rod is in equillibitium, it is parallel to the wall. Calculate the period of the oscillations that result when the rod is rotated slightly and released

Explanation / Answer

you have not provided the pic

this is a case of torsional pendulum

in case of torsional pendulum w = root (k/I)

w = angular frequency

K = spring constant

I = moment of inertia

I about centre = ml^2/12 = 3x .5x .5 /12 = 0.0625 kgm^2

k = 1 N/m

w = root (1 / 0.0625)

w = 4 rad/s

linear frequency = f

we know that

2 x pi x f = w

f = w / 2 x pi

f = 0.6366 Hz

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