00:01
Hello students in this question we have a rigid surface like this and then there is a spring here and the spring is connected to another rigid surface and the springs can move in horizontal and vertical directions.
00:20
They both have the stiffness constant k and gravity acts.
00:26
So we need to find out the equation of motion here.
00:28
So this road has a mass of m and this length is l right given.
00:35
So what we can do is that we can write down the equation of motion.
00:41
So this is the first gravitational force acting on here.
00:45
So this this this force the gravitational force let's take the center of mass the center and the mg force will be acting in here.
00:54
So the normal force act in this direction.
00:58
So normal force will be acting in this direction and it has to be resolved.
01:02
So we have the springs restitution force of spring acting in this direction.
01:10
So we can write down that it will be equal to kx.
01:15
Kx will act on to the bottom direction with a minus sign and the this gravitation this is the fs and the gravitational force fg will be acting towards the bottom from the center.
01:30
So let's take that as take that as mg right mg from the center.
01:39
Ok now this will have a horizontal force.
01:43
This will have a horizontal restitutional force it will keep it from not moving in the horizontal direction.
01:49
So that will be the only capable thing this can do.
01:53
So this will be another fs horizontal fs horizontal.
01:59
This is vertical.
02:01
Fs horizontal will be equal to in this direction to the right left side.
02:05
So that will be equal to minus fsh sorry that is equal to minus kx again.
02:16
Ok some displacement we don't know the displacement exact displacement.
02:20
So we are taking it to be equal in this case equal to x some x displacement happens.
02:26
Now the balancing kind of thing what happens is that the balancing occurs when let's take the this vertical distance as y that we can replace it as y and horizontal as x.
02:42
So this is the displacement in vertical direction and this is the displacement in horizontal direction...