A physica pendulum is constructed from a uniform thin rod oflength L suspended f

Question

A physica pendulum is constructed from a uniform thin rod oflength L suspended from one end. The center of gravity forsuch a rod lies at the midpoint of its length. (table 9.1 would behelpful) A)Derive the equation of motion for this physical pendulumand, from that, determine its period and angular frequency,assuming only small angle oscillations. B) What would be the length of a simple pendulum that has thissame period? Hint: Gravity is the only force acting on the pendulum and, bydefinition, can be considered to be acting at its center ofgravity. please provide a free body diagram. A physica pendulum is constructed from a uniform thin rod oflength L suspended from one end. The center of gravity forsuch a rod lies at the midpoint of its length. (table 9.1 would behelpful) A)Derive the equation of motion for this physical pendulumand, from that, determine its period and angular frequency,assuming only small angle oscillations. B) What would be the length of a simple pendulum that has thissame period? Hint: Gravity is the only force acting on the pendulum and, bydefinition, can be considered to be acting at its center ofgravity. please provide a free body diagram.

Explanation / Answer

Consider a meter stick which is pivoted at one end then the torque acting on it is     = -L( Fg sin)    I = - L (mgsin)     = - mgL / I   ( for small angles sin ˜ ) then Time period T = 2 / =2 ( / ) = 2 (I / mgL) Here I is the moment of inertia which is              I = 1/3 mL2 therefore Time period T = 2 ( 1/3mL2 ) / mg( 1/2L ) = 2 (2 L/3g ) angular frequency = 2 /T = ( 3g/2L) (b) If simple pendulum have same time period            T = 2 (2 L /3g )            2 ( l /g ) = 2 (2 L /3g )     then length of the simplependulum  l = 0.82 L

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