00:01
Hello student according to the question we have a given mass is 2 kg and here we have such the mass of 2 kg suspended from a spring that is spring constant it is given that is spring constant spring constant it is equal to 10 newton per meter.
00:24
Now it is then set in the motion it gives the initial velocity 150 centimeter per second and we have to find the expression of motion of mass assuming no error distance.
00:34
Now according to the question it is here that is we have to assume that is position of the mass at this point that is x equal to 0.
00:42
So initial velocity it is given initial velocity it has given that is 150 centimeter per second this mean that the mass is displaced from its equilibrium position and start moving.
00:58
So that we can assume that displacement of the mass at the point is x is equal to a.
01:06
So let us suppose the displacement here that is x is equal to a where a is the amplitude of the motion.
01:22
Now we know that the spring constant it is given that is 10 newton per meter.
01:27
So as we know there is force f is equal to minus kx that is for the formula for the spring force.
01:34
Now where x is the displacement of the mass from equilibrium position and k where negative sign indicates that force is in the opposite direction of the displacement.
01:45
Now also here mass is subjected to the under to the gravity.
01:50
So as we know f is equal to mg that is m the mass and g the acceleration due to gravity g is equal to 9 .8 meter per second square.
02:02
Now the net force acting on the mass is the sum of the force due to the spring and the gravitational constant.
02:08
So we have f net is equal to minus of kx plus mg.
02:17
Now by using the newton's second law of motion by newton's newton's second law of motion.
02:32
So here we can write f is equal to mass into acceleration.
02:35
So now here we can write it as that is this term here that is equal to mass into acceleration is equal to minus kx plus mg which can be arranged in the form of acceleration.
02:51
So in terms of acceleration we can write it as k is equal to minus k divided by m that is multiplied by x and this is plus of g...