Answer:
The potential energy of the system is [tex]\dfrac{E}{4}[/tex].
Explanation:
Given :
Mass of object , m .
Spring constant , k .
Total energy , E .
Maximum displacement , A .
We have to find potential energy when its kinetic energy is equal to 3/4E .
Now, we know :
Total energy is constant in simple harmonic motion.
Therefore ,
Total energy = Kinetic energy + potential energy .
[tex]E=P.E+\dfrac{3E}{4}\\\\P.E=\dfrac{E}{4}[/tex]
Hence , this is the required solution.
