00:01
Hello students, we have a mass connected to a spring.
00:05
So this is the mass.
00:06
So the mass m is equal to 0 .5 kilograms and the spring constant k for the spring is given to be equal to 20 newton per meter.
00:17
So this oscillates in a track.
00:20
So we need to find out the total energy.
00:24
So this extreme situation when it is at the maximum displacement and at the minimum displacement two conditions are there and at the equilibrium.
00:32
So this is the equilibrium position.
00:34
So the displacement is x.
00:37
So we can say the energy will be equal to the potential energy will be equal to half k x square.
00:44
That is the maximum.
00:46
So this will be equal to at the equilibrium.
00:49
It will be equal to kinetic energy which is equal to half m v square.
00:55
Right.
00:55
So this is the term that we are after.
00:58
Right.
00:58
At this point, there is no potential energy because the displacement is going to be zero.
01:02
And at this point, the kinetic energy will be maximum will be zero at this point.
01:09
So k is equal to zero here.
01:11
P is equal to zero here.
01:14
So the total energy at an instant will be equal to p plus k that will be equal to either half k x square or half m v square.
01:27
So to find out the energy, we have the mass and the the the other thing mass and the spring constant.
01:38
So we can say half and half can be cancelled each other.
01:41
So you will get k which will be equal to k is given as 20 times x square must be equal to m which is zero point zero five.
01:52
So zero point five times v square.
01:57
So x square by v square.
01:59
We can say 20 20 by zero point five.
02:07
So this is one by two.
02:09
That is 40 must be equal to v square by x square.
02:14
So v square by x square is equal to 40...