(Solved): The voltage pulse shown in is applied to the ideal integrating amplifier shown in Take ...

The voltage pulse shown in is applied to the ideal integrating amplifier shown in Take \( v_{o}(0)=0 \). Derive the numerical expression for \( v_{o}(t) \) for the time interval \( t<0 \). Express your answer in terms of \( t \), where \( t \) is in seconds, and the result is in volts. Derive the numerical expression for \( v_{o}(t) \) for the time interval \( 0 \leq t \leq 50 \mathrm{~ms} \). Express your answer in terms of \( t \), where \( t \) is in seconds, and the result is in volts. Derive the numerical expression for \( v_{o}(t) \) for the time interval \( 50 \mathrm{~ms} \leq t \leq 100 \mathrm{~ms} \). Express your answer in terms of \( t \), where \( t \) is in seconds, and the result is in volts. Derive the numerical expression for \( v_{o}(t) \) for the time interval \( 100 \mathrm{~ms} \leq t \). Express your answer in terms of \( t \), where \( t \) is in seconds, and the result is in volts.