A system initially at rest satisfies $0.01y\prime\prime(t)+0.2y\prime(t)+y(t)=6x(t)$, with t in seconds. A unit step is applied at t=0. Find |y(1)| to two decimal places.
The transfer function is 6/(.01s²+.2s+1)=600/(s+10)². The unit-step response is y(t)=6[1−(1+10t)e⁻¹⁰ᵗ]. At t=1 this gives 6[1−11e⁻¹⁰]=5.9970, rounding to 6.00. The repeated real pole gives a critically damped response.
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