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  1. The magnitude of average accleration in halt time period in a simple harmonic motion is(ans:2Aw^2/pi).

Asked by saraswatmajumder 16th March 2018, 12:28 AM
Answered by Expert
Answer:
begin mathsize 12px style E q u a t i o n space o f space S H M colon space minus space space x space equals space A space sin left parenthesis omega t right parenthesis semicolon space w h e r e space A space i s space a m p l i t u d e space a n d space omega space i s space a n g u l a r space f r e q u e n c y

a c c e l e r a t i o n space fraction numerator d squared x over denominator d t squared end fraction space equals space minus a omega squared sin left parenthesis omega t right parenthesis space
a v e r a g e space a c c e l e r a t i o n space o v e r space h a l f space p e r i o d less than fraction numerator d squared x over denominator d t squared end fraction space greater than space space space equals space 2 over T left parenthesis negative a omega squared right parenthesis integral subscript 0 superscript bevelled T over 2 end superscript sin left parenthesis omega t right parenthesis d t space equals space 2 over T left parenthesis negative a omega squared right parenthesis open parentheses fraction numerator negative 1 over denominator omega end fraction close parentheses space left parenthesis negative 2 right parenthesis

less than fraction numerator d squared x over denominator d t squared end fraction space greater than space equals space fraction numerator negative 4 a omega over denominator T space end fraction space equals space fraction numerator negative 4 a omega over denominator begin display style bevelled fraction numerator 2 pi over denominator omega end fraction end style space end fraction space equals space fraction numerator negative 2 a omega squared over denominator pi end fraction

end style
Answered by Expert 16th March 2018, 12:08 PM
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