Saved Bookmarks
| 1. |
A particle oscillates according to the law s=(1+cos^(2)t+cos^(4)t)sin500t Expand this motion into its harmonic components and plot its spectrum. |
|
Answer» Solution :We have `1+cos^(2)t+cos^(4)t=1+(1)/(2)(1+cos2t)+(1)/(4)(1+cos2t)^(2)=` `=(1)/(4)[7-4cos2t+(1)/(2)(1cos4t)]=(1)/(8)(15+8cos2t+cos4t)` HENCE `s=(1)/(8)(15-8cos2t-cos4t)sin500t(15)/(8)sin500t+cos2tsin500t+` `+(1)/(8)cos4t.sin500t=(15)/(8)sin500t+(1)/(2)sin502t+(1)/(2)sin498+(1)/(16)sin504t+(1)/(16)sin496t` The spectrum of the vibrations CONSIDERED above is SHOWN in FIG 
|
|