In `y = Asinomegat + Asin(omegat + (2pi)/(3))`
`|{:(,"Column-I",,"Column-II"),((A),"Motion",(p),"is periodic but no SHM"),((B),"Amplitude",(q),"is SHM"),((C),"Initial phase",(r),A),((D),"Maximum velocity",(s),pi//3),(,,(t),omegaA//2),(,,(u),"None"):}|`

Explanation

To solve the problem, we need to analyze the given equation of motion and determine the corresponding values for each item in Column I based on the information provided in Column II.

### Step-by-Step Solution:

1. **Given Equation**:
The equation provided is:
\[ y = A \sin(\omega t) + A \sin\left(\omega t + \frac{2\pi}{3}\right) \]

2. **Combine the Sine Terms**:
We can factor out \(A\) from the equation:
\[ y = A \left( \sin(\omega t) + \sin\left(\omega t + \frac{2\pi}{3}\right) \right) \]
Using the sine addition formula, we can simplify this further.

3. **Using Trigonometric Identities**:
We apply the identity:
\[ \sin A + \sin B = 2 \sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right) \]
Here, let \(A = \omega t\) and \(B = \omega t + \frac{2\pi}{3}\):
\[ y = A \cdot 2 \sin\left(\omega t + \frac{\pi}{3}\right) \cos\left(\frac{\frac{2\pi}{3}}{2}\right) \]
Since \(\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}\), we have:
\[ y = A \cdot 2 \cdot \frac{1}{2} \sin\left(\omega t + \frac{\pi}{3}\right) = A \sin\left(\omega t + \frac{\pi}{3}\right) \]

4. **Identify the Motion**:
The equation \(y = A \sin(\omega t + \phi)\) is in the standard form of simple harmonic motion (SHM). Thus:
- **Motion**: It is periodic and represents SHM.
- Corresponding option: **A corresponds to q** (Motion is periodic but no SHM).

5. **Determine Amplitude**:
From the equation \(y = A \sin(\omega t + \frac{\pi}{3})\), the amplitude \(A\) is clearly:
- **Amplitude**: \(A\)
- Corresponding option: **B corresponds to r** (Amplitude is SHM).

6. **Determine Initial Phase**:
The initial phase \(\phi\) in the equation is \(\frac{\pi}{3}\):
- **Initial Phase**: \(\frac{\pi}{3}\)
- Corresponding option: **C corresponds to s** (Initial phase is \(\frac{\pi}{3}\)).

7. **Calculate Maximum Velocity**:
The maximum velocity \(V_{\text{max}}\) for SHM is given by:
\[ V_{\text{max}} = A \omega \]
Since this does not match any of the options provided, we conclude:
- **Maximum Velocity**: \(A \omega\)
- Corresponding option: **D corresponds to u** (None).

### Final Correspondences:
- A corresponds to q
- B corresponds to r
- C corresponds to s
- D corresponds to u