00:01
Hello, here we have a given that is d2y divided by dt square plus 12 dy divided by dt plus of 32y is equal to that is 32x of t.
00:17
Now assuming that input it is given, assuming the input it is given by that is x of t is equal to u of t.
00:33
So, equation can be written as that is d2y divided by d2 square plus 12 dy divided by dt plus of 32y is equal to this can be written as 32 u of t.
00:49
So, here in place of x of t this is it is given that is u of t, u of t.
00:58
So, in place of this we can write x of t.
01:01
Now, taking the laplace transform, taking the laplace transform, so here we can get it as that is laplace transform of d2y divided by dt square.
01:14
So, this can be written as that is s square multiplied by y of s now plus of 12 s multiplied by y of s plus 32 y of s that is equal to 32 x of s.
01:36
Now, from here taking y as common, so this can be written as y of s.
01:41
So, this is multiplied by s square plus 12 s plus 32 this is equal to here we have 32 multiplied by x of s.
01:54
Now, shifting this term into the right side and x of s into the left side, so this can be written as that is x y of s this is divided by x of s this is equal to 32 which is divided by s square plus 12 s this is 12 s plus 32.
02:20
So, in the first part we have to find the transfer function.
02:23
So, this is the transfer function.
02:26
So, finally from here we hence we get the transfer function that is equal to h of s hence from here we have h of s is equal to 32 divided by s square plus 12 s plus 32.
02:48
So, this is the answer for the first part.
02:50
Now, if we plot the 0, so here for the b part this is for the a part...