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In Fig. 15.33, a stick of length L= 1.65...

In Fig. 15.33, a stick of length L= 1.65 m oscillates as a physical pendulum. (a) What value of distance x between the stick's center of mass and its pivot point O gives the least period? (b) What is that least period?

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x= 0.48m, (b) T= 2.0s
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In physical pendulum, the time period for small oscillation is given by T=2pisqrt((I)/(Mgd)) where I is the moment of inertial of the body about an axis passing through a pivoted point O and perpendicular to the plane of oscillation and d is the separation point between centre of gravity and the pivoted point. In the physical pendulum a speacial point exists where if we concentrate the entire mass of body, the resulting simple pendulum (w.r.t. pivot point O) will have the same time period as that of physical pendulum This point is termed centre of oscillation. T=2pisqrt((I)/(Mgd))=2pisqrt((L)/(g)) Moreover, this point possesses two other important remarkable properties: Property I: Time period of physical pendulum about the centre of oscillation (if it would be pivoted) is same as in the original case. Property II: If an impulse is applied at the centre of oscillatioin in the plane of oscillation, the effect of this impulse at pivoted point is zero. Because of this property, this point is also known as the centre of percussion. From the given information answer the following question: Q. If an impulse J is applied at the centre of oscillation in the plane of oscillation, then angular velocity of the rod will be .

In physical pendulum, the time period for small oscillation is given by T=2pisqrt((I)/(Mgd)) where I is the moment of inertial of the body about an axis passing through a pivoted point O and perpendicular to the plane of oscillation and d is the separation point between centre of gravity and the pivoted point. In the physical pendulum a speacial point exists where if we concentrate the entire mass of body, the resulting simple pendulum (w.r.t. pivot point O) will have the same time period as that of physical pendulum This point is termed centre of oscillation. T=2pisqrt((I)/(Mgd))=2pisqrt((L)/(g)) Moreover, this point possesses two other important remarkable properties: Property I: Time period of physical pendulum about the centre of oscillation (if it would be pivoted) is same as in the original case. Property II: If an impulse is applied at the centre of oscillatioin in the plane of oscillation, the effect of this impulse at pivoted point is zero. Because of this property, this point is also known as the centre of percussion. From the given information answer the following question: Q. For the above question, locate the centre of oscillation.

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The time period of a physical pendulum about some pivot point is T. When we take another pivot point, opposite of the first one such that the centre of mass of the physical pendulum lies on the line joining these two pivot points, we obtain the same time period. If the two points are separated by a distance L, then the time period T is

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