A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions, find the phase difference between the individual motions.

Explanation

To solve the problem, we need to find the phase difference between two simple harmonic motions (SHMs) that have equal amplitudes and equal frequencies, given that the resultant amplitude is equal to the amplitude of the individual motions.

### Step-by-Step Solution:

1. **Define the Amplitudes**:
Let the amplitude of the first SHM be \( A_1 = A \) and the amplitude of the second SHM be \( A_2 = A \), since they are equal.

2. **Resultant Amplitude**:
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