Answer:
The system's potential energy is [tex]\frac{kA^{2} }{8}[/tex]
Explanation:
The total mechanical energy of the system is E which the sum of the potential energy and the kinetic energy.
The total energy of a simple harmonic oscillator is given as E = [tex]\frac{1}{2}kA^{2}[/tex].
The system's kinetic energy is given as [tex]\frac{3}{4} E[/tex]
Total system Energy (E) = Potential Energy (P) + Kinetic Energy (K)
E = P+K
P = E - K
P = [tex]\frac{1}{2}kA^{2} - \frac{3}{4}E[/tex]
P = [tex]\frac{1}{2} kA^{2} - \frac{3}{8} kA^{2}[/tex] = [tex]\frac{kA^{2} }{8}[/tex]
Potential Energy (P) of the system = [tex]\frac{kA^{2} }{8}[/tex]
