00:01
Hi, here in this given problem there is a simple pendulum whose length is given as effective length of the simple pendulum that is l is equal to 2 .23 meter.
00:26
Here, mass of the bob attached with 8 that is given as 6 .74 kilogram initial speed of the bob at the mean position will speed at the mean position that is given as let it be represented as v i and that is 2 .06 meter per second and that initial speed at the mean position it will be taken as the maximum possible speed of the oscillating simple pendulum.
01:22
Now in the first part of the problem, here we have to find time period of this simple pendulum.
01:29
That time period of the simple pendulum is given by an expression.
01:34
T is equal to 2 pi square root of l by g.
01:39
This is 2 times of 3 .14 square root of length, which is 2 .3 divided by 9 .8 meter per second is square so this time period comes out to be equal to 2 .995 second or we can say approximately this is 3 .0 second which is the answer for the first part of the problem now in the second part of the problem we have to find total energy associated with this simple pendulum and that total energy will actually be equal to its maximum kinetic energy which is at the mean position.
02:30
So that maximum kinetic energy at the mean position, it will be given by a simple expression for the kinetic energy, half mv i square.
02:53
So plugging in the known values here, this is half into 6 .74 into 2 .06 square.
03:03
And here this energy, the total energy of the simple pendulum e comes out to be equal to 14 .3 jules, which becomes the answer for the second part of the problem.
03:18
Now, in the third part of the problem, we have to find the angular displacement for the maximum high at the extreme position where the bob will come to rest.
03:33
Momentarily.
03:35
So here if we look the diagram of this simple pendulum, this was its mean position, then it is displaced.
03:47
And suppose here it comes to rest momentarily like this.
03:52
This will be the maximum possible angular displacement theta.
03:59
This is the height, vertical height, this is the length l.
04:05
So if we consider a right angle triangle here this initial position is represented as a, this extreme position is represented as b and this point be taken as c...