A body of mass 2 kg is executing simple harmonic motions according to the cquation 0.06 cos (100t+ `pi//4` ) m, where t is in seconds. What is the maximum kinetic energy?

Explanation

To find the maximum kinetic energy of a body executing simple harmonic motion (SHM), we can follow these steps:

### Step 1: Identify the parameters from the SHM equation
The given equation of SHM is:
\[ y = 0.06 \cos(100t + \frac{\pi}{4}) \]
From this equation, we can identify:
- Amplitude \( A = 0.06 \, \text{m} \)
- Angular frequency \( \omega = 100 \, \text{rad/s} \)

### Step 2: Calculate the maximum velocity
The maximum velocity \( V_{\text{max}} \) in SHM is given by the formula:
\[ V_{\text{max}} = A \omega \]
Substituting the values we found:
\[ V_{\text{max}} = 0.06 \, \text{m} \times 100 \, \text{rad/s} = 6 \, \text{m/s} \]

### Step 3: Use the formula for maximum kinetic energy
The maximum kinetic energy \( KE_{\text{max}} \) is given by the formula:
\[ KE_{\text{max}} = \frac{1}{2} m V_{\text{max}}^2 \]
Where \( m \) is the mass of the body. Given that \( m = 2 \, \text{kg} \), we can substitute the values:
\[ KE_{\text{max}} = \frac{1}{2} \times 2 \, \text{kg} \times (6 \, \text{m/s})^2 \]

### Step 4: Calculate the maximum kinetic energy
Now, calculating the maximum kinetic energy:
\[ KE_{\text{max}} = 1 \times 36 \, \text{J} = 36 \, \text{J} \]

Thus, the maximum kinetic energy of the body is:
\[ \boxed{36 \, \text{J}} \]

---