00:01
So, this is the pulley here and here a spring is connected to the wall then a mass is attached to the pulley here the mass m.
00:20
So, the mass moment of inertia is i naught of the pulley.
00:27
So, for the mass m for mass m we have the tension is towards upward and in downward direction it is forced due to the gravity.
00:45
So, we can write the equation mg minus t is equals to ma.
00:53
So, t is equals to and a we know that v is x naught and a is x double dash v is x dash let us say v is x dash and a is x double dash.
01:18
So, minus of mx double dash plus mg.
01:25
So, we have t is equals to m whole into g minus x double dash.
01:33
So, for spring force f is equals to kx here x is equals to 4r theta x is equals to 4r theta.
01:49
So, force is equals to 4k r into theta.
01:55
So, torsional equilibrium is that is here the here one here this is the pulley and here in this direction the force that is f of spring and here due to the tension.
02:21
So, x is equals to r into theta v is equals to r into theta dash and a is equals to r into theta double dash.
02:38
So, here we can write j naught into theta double dash is equals to t into r minus 4k r theta whole to the power 4r...