Observe that the given vector field is a gradient field:
Let , so that
Integrating the first equation with respect to , we get
Differentiating this with respect to gives
Now differentiating with respect to
gives
Putting everything together, we find a scalar potential function whose gradient is ,
It follows that the curl of is 0 (i.e. the zero vector).
Answer:
Explanation:
General Equation of SHM is given by
where x=position of particle
A=maximum Amplitude
angular frequency
t=time
At any time Total Energy is the sum of kinetic Energy and Elastic potential Energy i.e.
where k=spring constant
Potential Energy is given by
also it is given that Potential Energy(U) is equal to Kinetic Energy(K)
Total Energy
Total
at
velocity is