Question

Laplace transfer functions and ODE?

1) Here is a differential equation. Please find the Laplace transfer function C(s)/R(s). Note that Initial conditions are zero.

***answer provided, please show work

dct) 9, ... - 4 20rc and²c(t) , - dt2 CE) 2 dct) dr(t) . - + 20r(t) + 5 - 2- d+3 dt dt²

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2) Here is a Laplace transfer function. Please find the corresponding ODE.

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Answer 1

Given differential equation is- dŁ2 d3clt) +5d²ect) - gacct = d²r(t +26rct) at att de given initial condition are zero so codzo dc at t=0=0 rion=0 dr at t=0 =0 at by la place transform - s ces + 56²cess-gsus) = R(S) + 2OR(S) so ccs) = Reso 8² +20 35s²-gs ! RUS) given PCSO = CCS) = S +4 - RCS) 84+1 so sheesh + cc so= 8²R(S) + 4R(S) by inverse lipeace transform- ducets ccts = d²rets turct). I dtu dt² property - if sects LT, XCS) - sêncts LT , & xcs) se act) is n time derivative with respect to 'to