A particle executes simple harmonic motion with an amplitude 9 cm. At what displacement from the mean position, energy is half kinetic and half potential ?

Explanation

To find the displacement from the mean position where the energy of a particle executing simple harmonic motion (SHM) is half kinetic and half potential, we can follow these steps:

### Step 1: Understand the total energy in SHM
The total mechanical energy (E) in simple harmonic motion is constant and is given by the formula:
\[ E = \frac{1}{2} k A^2 \]
where \( k \) is the spring constant and \( A \) is the amplitude of the motion.

### Step 2: Set up the condition for half kinetic and half potential energy
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