00:01
Hello students, in order to find the transfer function g of s for the mechanical system you can see there is a moment of inertia of this thing is given so there is a spring system and a damping mechanism is connected to that.
00:18
So this is the damping mechanism and further this is connected to a rotational torque theta 2 or rotational momentum and then further a damping system and a spring and a surface right.
00:38
So the damping coefficient so we are given that g of s is equal to we can find out g of s will be equal to output angular velocity theta s divided by input torque ts.
00:51
So input torque is given here so we are given that the moment of inertia i is equal to 1 kilogram meter square and we are given the damping coefficient f is equal to 1 newton meter square.
01:13
So now using the newton's second law of motion we can write down that t of s which is torque minus f theta of s will be equal to i times d theta of s by dt right.
01:38
Here t is the torque f is the friction damping coefficient and i is the moment of inertia and d theta by dt is the time rate of change of angular velocity.
01:54
So now we can express the output angular velocity theta s will be equal to t of s divided by i times s plus f.
02:08
How because we can take the laplace transform of this thing.
02:12
So let's take that laplace transform of this thing so let's take it so you get laplace transform of this component so you'll get t of s laplace transform of t of s is again t of s minus f times theta of s must be equal to i times s theta of s right.
02:38
So you can write down t of s will be t of s minus or we can write down theta of s theta of s will be equal to t of s divided by i times s minus s plus f...