question_answer

                A particle of mass m oscillates with simple harmonic motion between points \[{{x}_{1}}\] and \[{{x}_{2}}\] the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph:           

A)                  

B)                                    

C)                             

D)                

Correct Answer: C

Solution :

                Potential energy is given by                 \[U=\frac{1}{2}k{{x}^{2}}\]                 The corresponding graph is shown in figure.                                 At equilibrium position (x = 0), potential energy is minimum. At extreme positions \[{{x}_{1}}\] and \[{{x}_{2}}\], its potential energies arc                 \[{{U}_{1}}=\frac{1}{2}\,kx_{1}^{2}\,and\,\,{{U}_{2}}=\frac{1}{2}\,kx_{2}^{2}\]                 Note: In the above graph, the dotted line (curve) is shown for kinetic energy. This graph shows that kinetic energy is maximum at mean position and zero at extreme positions \[{{x}_{1}}\] and \[{{x}_{2}}\].