00:01
Hello students here we have a spring mass system that is moving in a circular path.
00:04
So from this we have to determine the lagrangian of the system.
00:07
In section a we have to write down the lagrangian.
00:15
So here in order to determine the lagrangian we need to know about the kinetic energy and potential energy.
00:23
The kinetic energy t that is equal to half m r square omega square.
00:31
This is our equation number one and the potential energy v is v equal to 1 by 2 r minus x the whole square into k.
00:47
This is our equation number two.
00:49
From this we can write down the equation of motion for the lagrangian.
00:55
So l equal to t minus v.
00:59
So here we can write the l that is equal to half m r square omega square minus half r minus x the whole square into k.
01:15
So from this we can get l that is equal to 1 by 2 m r square omega square minus 1 by 2 k r minus x the whole square.
01:33
This is our equation number three and this is the lagrangian of the system.
01:41
From this in section b we have to determine the equation of motion.
01:50
That is we can write down the equation of motion from lagrangian.
02:01
So the equation is here d by dt of dou l divided by dou omega minus dou l divided by dou x that is equal to zero...