00:01
In this problem, we have been given the potential energy of an object which is undergoing simple harmonic motion represented by u equals half k x square.
00:11
And this potential energy, it's a function of the position x here.
00:16
And assuming the mass of the object as m and at t equal to zero, the object is present at the equilibrium position denoted by x equals to zero.
00:27
And taking omega as root k by m, we are required to get the equation of motion that's the displacement as a function of time t.
00:37
This is what we need to determine.
00:40
So we know that the work that is being done on the object as it undergoes simple harmonic motion.
00:47
That is negative change in potential energy.
00:51
So basically the work done, that's also negative.
00:54
So we can see that the work done it's half kx square and we have this expression for work because this force is variable force and let's use that expression so we can get integral f dot dx is equal to half kx square and from here we can get the force by just differentiating the term on the right hand side so on differentiating we get the force as kx so that's the magnitude of force and this is also right in accordance with hooke's law.
01:28
And we know that the force can be written as mass times the acceleration.
01:32
So m -e will be k times x, and that implies a will be k -by -m times x...