00:01
In question we have to give a second order system and in this system peak time that is tp.
00:17
So, at this peak time this is defined this is the time tp where y is equal to y max where the value of y should be equal to y max.
00:37
So, the output of second order system that will be equal to yt that is equal to k into 1 minus e raised to the power minus jt multiplied by cos wdt plus swn divided by wd into sin wdt.
00:58
So, this is the equation here.
01:00
So, from here dy divided by dt will be equal to k into e raised to the power e omega into n divided by under the root 1 minus epsilon square into sin omega dt.
01:16
So, we know that at y at tp that means maximum peak that should be equal to 0 that means wp into tp that should be equal to y.
01:26
So, that means from here tp will be equal to pi divided by wp.
01:31
So, by putting this value we have that given in the question that tp is less than tp dash.
01:40
So, tp is equal to pi by omega t.
01:43
So, this is less than tp dash...