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:              [AIPMT 2003]

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 \[{{x}_{2}}\].