GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 30 of 65

Marks: +1, -0

The solution of

\;{ {d}^{2} {y}}/{ {dt}^{2}}- {y}=1

, which additionally satisfies

{y}|_{ {t}-0}=\;{ {d} {y}}/{ {dt}}|_{ {t}-0}=0

in the Laplace s-domain is

Solution:

\;{d^{2} y}/{d t^{2}}-y=1

and

{y}|_{ {t}=0}=\;{ {dy}}/{ {dt}}|_{ {t}=0}=0

{L}\{\;{d^{2} y}/{d t^{2}}\}-L(y)=\;{1}/{S}

{s}^{2} {F}( {S})- {Sf}(0)- {f}^{'}(0)- {F}( {s})=\;{1}/{ {S}}

{F}( {s})\{( {S}-1)( {S}+1)\}=\;{1}/{ {S}}

{F}( {S})=\;{1}/{ {S}( {S}-1)( {S}+1)}

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