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3. The magnitude of average acceleration in half time period in a simple harmonic motion is(A) 2 ω2A /π(B) ω2A /2 π(C) ω2A /√2 π(D) Zero

Avik Das , 8 Years ago
Grade 12th pass
anser 1 Answers
dip
average acceleration=∫adt/∫dt
let equation be x=Asinwt
therefore equation of  acceleration a=-Aw2sinwt
average acceleration =\int_{0}^{T/2}-Aw^{2}sinwt
                                                                     
                                \int_{0}^{T/2}dt
 
 
=\frac{-2Aw^{2}}{T}\frac{1}{w}\int_{0}^{T/2}-coswt
 
=\frac{2Aw}{T}[coswT/2-cos0]
 
 
T=\frac{2\pi }{w}
=-\frac{2Aw^{2}}{\pi }
 
ans:a
 
 
 
 
Last Activity: 8 Years ago
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