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The dynamics of a spring-damper-mass system is defined by the following differential equation, č + 4€ + 5x = f(t),x(0) = 1, *

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Before solving questions we should have to know some formulas LT {g} - Slity) -Yo LT > Laplace Tractory LT { M} = SLTg-syco)-i tun+ 50 Act x(0)=), Co=2 2ct) - louet) do taking Laplace of both orde Š LT(X) - SACC)- x0) + 4 LT(X) - Mo) +5&T(X) = LT Louclassmate Date Page So we get the Laplan L160) >> XC9) = 3 +235 +10 s [5°+45+5) by taking Inverse Caplace Transform will getکودک- وبا در تما+3+ [(x) = het) - It grest5-st5 (54 عادی )5 lit ک- الا - 5 )5 الأدب و ادی)5 لوط عين * زباله = [] می دارد )۲ بmate sney)= U4) - fe costat 7 fe sint at Il le costat have usv-fansu) I et Sint- de sint I e sintet af etsint i z e Bint tosimbadly it at sint de at In eat the cost - 94 r-cost- 1-20 x-Cost detto-cost sut-1-20 sht -- e cost-alea 1 st 4 I 2 = -e cosSint-rest- frost-) estat not a 14 - 4 2/5 + 1/5 [13sint + a cost] - $15 cate [1359) + a cast]Updated the answer

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