Question

Q1. Mass M is lifted by a pulley system as shown in Figure 1. The pulley is rotating in a clockwise direction. Assuming zero initial conditions, obtain transfer function of the system, X(s)/Ta(s). Τα B X м k Figure 1

Answer 1

can be redrawn as (for understanding Ta (Pa Sol The givean system Kimelic emergylt) 4k eftk Epuney T= 1Kx² + Ź Jo² Potential energy ergy (u)- (P.E. e poing U= 1 koc? Dissipation function ()=12.842 1. B T! n=1 (a damper I Boca :.0=RO O=0c Total energy hergy (L)=T+U = Im sch+ 1 I oc 2 + 1 Koc? = -1 Comt 1 - 2 ) oc² + 1 Koc? By tagarangan lagrangiam theonem, the equation of motion is (1) + do tada d (2) = Ta dL dD - Boc, dL = kx doc M+ I doc doc + Boć tkoc= Ta equation of motion Apply.laplace troansform to equo L { + 7 ) se } + 2 {Boe} + L {koe} = L{Ta}

Note: Luis = sx() - costo Loc? = x 6) L{sis = s2x) -460-63 L {Ta} = Tals) ]52x@+ 8sx(0)+ Kx)- Talia) Tao) x(o) [Em + 7 / 2] 32+ BS+K X(6) (M+I +BSTK R2 then we have to -)24+ Note: If conase of pulley consider translational kimetic energy of pulley Imse ² since here the pulley ie constrained the treens lotional, velocity ce=o).
Note:plzz don't give dislike....plzzzz comment if you have any problem i will try to solve your problem.....plzzzzz give thumbs up i am in need.....