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6 Oscillations
(a) Trolley moving horizontally with acceleration a
T
= T
g
g 2 + a 2
(6.22)
(b) Trolley rolls down on a frictionless incline at an angle θ to the horizontal plane
T
= T / cos θ
(6.23)
Physical Pendulum
Any rigid body mounted such that it can swing in a vertical plane about some axis
passing through it is called a physical pendulum, Fig. 6.1.
Fig. 6.1
The body is pivoted to a horizontal frictionless axis through P and displaced from
the equilibrium position by an angle θ . In the equilibrium position the centre of mass
C lies vertically below the pivot P. If the distance from the pivot to the centre of mass
be d, the mass of the body M and the moment of inertia of the body about an axis
through the pivot I , the time period of oscillations is given by
T = 2π
1
Mgd
(6.24)
The equivalent length of simple pendulum is
L eq = I /Md
(6.25)
The torsional oscillator consists of a flat metal disc suspended by a wire from a
clamp and attached to the centre of the disc. When displaced through a small angle