When displacement is one-third of the amplitude, what fraction of total energy is potential energy and what fraction is kinetic energy in simple harmonic motion ?

Explanation

To solve the problem of finding the fraction of potential energy and kinetic energy when the displacement is one-third of the amplitude in simple harmonic motion (SHM), we can follow these steps:

### Step 1: Understand the Definitions
In simple harmonic motion, the total mechanical energy (E) is the sum of kinetic energy (K.E) and potential energy (P.E). The total energy in SHM is given by:
\[ E = \frac{1}{2} m \omega^2 A^2 \]
where \( A \) is the amplitude, \( m \) is the mass, and \( \omega \) is the angular frequency.

### Step 2: Determine Displacement
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