Answer Happy

Suggestions: draw a graph with approximate scales, showing the interrelation, indicate the switching points as: on: t=to; grow exponentially until: t=t₁; run freely until: t=t₂; decrease exponentially and switched off: t=t3. Make necessary additions to the axes system indicating the units and quantities. Use the step function u(t) for switching the base functions on and off. Please, pay attention to the correct positions of the sinusoidal and exponential curves on the time axis. 3 0 6 7.5 -3

A sinusoidal signal of the form v(t) = 3.cos(ot) is switched on at t=0 and grows enveloped exponentially with a time constant + = 3T to its maximum, afterwards it runs free (non-enveloped) for 3 periods, from the maximum of the third free period it declines again exponentially within one period down to 3t level and is then switched off. Please, formulate the sequence analytically and show it on a graph. You could represent based on T (the period) and you may take two units as T on the axes given below for your graph. For the solution of the task you definitely do NOT need the absolute value of . Refer your solution to T. Suggestions: draw a graph with approximate scales, showing the interrelation, indicate the switching points as: on: t=to; grow exponentially until: t-t₁; run freely until: t=t₂; decrease exponentially and switched off: t-t3. Make necessary additions to the axes system indicating the units and quantities. Use the step function u(t) for switching the base functions on and off. Please, pay attention to the correct positions of the sinusoidal and exponential curves on the time axis. 3 3 6 7.5 0 -3