InterviewSolution
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InterviewSolution
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A particle executes S.H.M with a period of 10 seconds. Find the time in which its potential energy will be half of its total energy. |
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Answer» Given : ` T = 10s ` Since, ` ( 1 )/( 2 ) ` T.E. = P.E. ` therefore ( 1 )/ ( 2 ) xx ( 1 ) /( 2 ) ka ^ 2 = ( 1 ) / ( 2 ) kx ^ 2 ` ` ( 1 ) /( 4 ) ka ^ 2 = ( 1 ) /( 2 ) kx ^ 2 ` ` rArr x = pm ( a ) /( sqrt 2) ` Also, ` x = a sin omega t ` ` a sin omega t = ( a ) /( sqrt2 ) ` ` sin omega t = ( 1 ) /( sqrt 2 ) ` ` sin ((2pi ) /( T) ) t = ( 1 ) / ( sqrt 2 ) ` ` sin ((2pi ) /( 10 ) ) t = ( 1 )/( sqrt 2 )" "[ because T = 10 `sec] ` ( pi ) /( 5 ) t = sin ^( - 1 ) (( 1 ) /( sqrt 2 ) ) ` ` (( pi ) /( 5)) t = ( pi ) /( 4 ) ` ` t = ( pi ) /( 4 ) xx ( 5 )/( pi ) ` ` t = 1.25 ` sec |
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