The model of a dynamic system is derived as [3 ddot{x}+7 dot{x}+2 x=50 sin t, x(0)=-1, dot{x}(0)=1]

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The model of a dynamic system is derived as

\[3 \ddot{x}+7 \dot{x}+2 x=50 \sin t, x(0)=-1, \dot{x}(0)=1\]

Find the system's total response, and identify the transient and steady-state responses.

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