Find the time period of small oscillations of the following systems. (a) A metre stick suspended through the 20 cm mark. (b) A ring of mass m and radius r suspended through a point on its periphery. (e) A uniform square plate of edge a suspended through a corner. (d) A uniform disc of mass m and radius r suspended through a point r/2 away from the centre.

(a) 1.51 s

(b)

(c)

(d)

(a) time period for a physical pendulum is given by

where’l’ is the distance between centre of mass and point of suspension

= 1.51 sec

(b)

when a ring is suspended through a point on its periphery,

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here l= r

(c)

when axis pass through corner of the square , we should consider moment of inertia in two directions

(d) uniform disc of a mass m and radius r suspended through a point r/2 away from center

Given l=r/2

=

1