Find the responses of systems governed by the following equations of motion for the initial conditions (x(0)=1,
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Find the responses of systems governed by the following equations of motion for the initial conditions \(x(0)=1, \dot{x}(0)=0\) :
a. \(2 \ddot{x}+8 \dot{x}+16 x=0\)
b. \(3 \ddot{x}+12 \dot{x}+9 x=0\)
c. \(2 \ddot{x}+8 \dot{x}+8 x=0\)
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