00:01
Hi, from the question given that a system is modeled as dy by dt plus a of y of t which is equal to b times of dx by dt plus cx of t.
00:17
Here a, b, c are all unknowns that is the thing we need to find here and the response to input x of t is equal to 9 plus 15 cos 12t and y of t is equal to 5 plus 13 cos 12t plus 0 .2487.
00:39
Now apply the laplace transform so sy of s is equal to plus not equal to plus a y of s is equal to bs x of s plus cx of s.
00:56
Now the system transfer function y of s by y of s by x of s is equal to bs plus c divided by s plus a.
01:10
So here so let s is equal to j omega so that b j omega plus c divided by j omega plus a.
01:24
So system gain absolute value of h of j omega is equal to square root of c square plus b square omega square divided by square root of a square plus omega square.
01:39
Therefore angle h of j omega is equal to tan inverse of omega b by c minus tan inverse of omega by a.
01:59
So gain of system here it is omega is equal to 0 so this implies absolute value of h of j of 0 is equal to c by a and c by a by comparing the given expression 5 by 9.
02:17
So this implies c is equal to 5 and a is equal to 9 and also gain of system omega is equal to 12.
02:26
Then absolute value of h of j omega is equal to square root of c square plus b square times of 144 divided by square root of a square plus 144.
02:43
So which is equal to 13 over 15...