00:01
So in this question y stands for amplitude of the base and wb means the base frequency.
00:10
Let's draw its diagram.
00:12
This is r plus m.
00:17
That's the string which has gone upwards.
00:26
This is a and this is b.
00:36
This is our diagram.
00:37
There is a foothold that is yt.
00:41
Now yt is equal to y sine wbt.
00:50
Steady state solution will be used here.
00:54
So alpha t will be equal to x cos wb into t minus, the steady state amplitude is x.
01:07
So x will be equal to y 1 plus 2 m plus 2 r whole square divided by 1 minus r square whole square plus 2 2 whole square.
01:34
Now this will be equal to the frequency ratio that is wm wn.
01:51
Here wm is equal to under root k upon m and 2 is equal to b upon z under root km.
02:10
Now zeta, the damping ratio, this is zeta of the damping ratio.
02:15
So x upon y will be equal to 1 plus 2 re whole square divided by 1 minus r square whole square plus 2 zeta r whole square.
02:35
Now if r is smaller than under root 2, then x upon y will be greater than 1...
