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What Is Compound Pendulum?
Compound pendulum: Compound pendulum is a rigid body of arbitrary shape suspended from a horizontal axis and free to oscillate in a vertical plane about the horizontal axis under the influence of gravity.
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Obtain The Equation Of Motion And The Time Period Of The Compound Pendulum.
Equation of motion of compound pendulum: Let us consider a compound pendulum is suspended in a vertical plane, from a horizontal axis through the point O as shown in the Fig.1. Let G be the centre of mass of the compound pendulum and be the distance of centre of gravity from the axis through the…
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Find The Length Of The Equivalent Simple Pendulum.
Equivalent simple pendulum: We know that the time period of oscillation of a compound pendulum is [ To know the derivation of this equation (CLICK HERE) ] where, is the acceleration due to gravity, is the distance between the centre of gravity and point , is the radius of gyration. If be the length of…
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Show That The Length Of A Simple Pendulum Equivalent To The Compound Pendulum Is L=I/Ml.
Equivalent simple pendulum: We know that the time period of oscillation of a compound pendulum is [ To know the derivation of this equation (CLICK HERE) ] where, is the acceleration due to gravity, is the distance between the centre of gravity and point , is the radius of gyration. If be the length of…
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Define Centre Of Suspension And Centre Of Oscillation.
Centre of suspension: Centre of suspension of a compound pendulum is a point where the vertical plane in which the compound pendulum oscillates, meets the horizontal axis of rotation of that compound pendulum.In Fig. 1, the point O is called the centre of suspension, where the horizontal axis of rotation of the compound pendulum meets…
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Show That The Centre Of Suspension And Centre Of Oscillation Are Reversible.
The centre of suspension and oscillation are reversible: In Fig. 1, the point O is called the centre of suspension, where the horizontal axis of rotation of the compound pendulum meets the vertical plane of oscillation of that compound pendulum. O’ is called the centre of oscillation for the given centre of suspension O of the compound pendulum,…
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Find The Condition For Minimum Time Period Of Oscillation Of Compound Pendulum, Find The Minimum Time Period.
Condition for minimum time period of compound pendulum: Let us consider a compound pendulum is suspended in a vertical plane from the horizontal axis through the point O and be the distance of the centre of gravity G from the centre of suspension O. So the time period oscillation of the compound pendulum is given…
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Show That A Uniform Rod Of Length ‘l’ Hanging As A Compound Pendulum From A Pivot At One End Has Same Frequency For Small Oscillation As A Simple Pendulum Of Length (2l/3).
Ans. The time period of the simple pendulum equivalent to a compound pendulum is given by, [ to know the derivation of the above equation (CLICK HERE) ] or, where, where, K is the radius of gyration, g is the acceleration due to gravity, is the length of the equivalent simple pendulum and is the…
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A Cube Of Edges ‘S’ And Mass ‘M’ Is Suspended Vertically From One Of Its Edges As The Axis Of Suspension. Find The Time Period Of Small Oscillation. What Is The Length Of Equivalent Simple Pendulum.
Ans. Let us consider a cube of mass and edges is suspended from one of its edges O as shown in the Fig. 1. The length of the diagonal of the cube of edges is If be the centre of gravity of the cube of side S, then . The moment of inertia of the…
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What Is The Distance Between The Centre Of The Suspension And Centre Of Oscillation Of A Uniform Cylindrical Metal Bar Used As A Second Pendulum.
Ans. If L be the distance between the centre of suspension and centre of oscillation of the compound pendulum then the time period of oscillation of the compound pendulum is where, is the acceleration due to gravity. For a second pendulum the time period of oscillation is 2 sec. therefore, or, or, cm or, cm
