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A particle vibrates according to the law s=(1+cos^(2)t+sint)sin500t Expand this motion into its harmonic components and plot its spectrum. |
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Answer» Solution :We have `1+cos^(2)t+sin^(4)t=1+(1)/(2)(1+cos2t)+(1)/(4)(1-cos2t)^(2)=(1)/(4)(4+2+2cos2t+1-2tcos^(4)2T` `=(1)/(4)[7+(1)/(2)(1+cos4t)]=(1)/(8)(15+cos4t)` Henec it follows `s=(1)/(8)+(15+cos4t)sin500t=` `=(15)/(8)sin500t+(1)/(8)sin500t.cos4t=` `=(15)/(8)sin500t+(1)/(16)sin504t+(1)/(16)sin496t` The spectrum is show in Fig 
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