STATEMENT-1`,` The total energy of a particle executing S.H.M( of given amplitude) of depends on the mass of particle but does not depend on its displacement from mean position
and
STATEMENT -2 `:` The total energy of a particle executing S.H.M. ismaximum at the mean position.

Answer

To analyze the given statements regarding the total energy of a particle executing Simple Harmonic Motion (S.H.M.), let's break down the problem step by step.

### Step 1: Understanding the Total Energy in S.H.M.
The total mechanical energy (E) of a particle in S.H.M. can be expressed with the formula:
\[ E = \frac{1}{2} m \omega^2 A^2 \]
where:
- \( m \) is the mass of the particle,
- \( \omega \) is the angular frequency,
- \( A \) is the amplitude of the motion.

### Step 2: Analyzing Statement 1
**Statement 1:** "The total energy of a particle executing S.H.M. of given amplitude depends on the mass of the particle but does not depend on its displacement from the mean position."

From the formula, we can see that:
- The total energy \( E \) does indeed depend on the mass \( m \) of the particle.
- The total energy is constant for a given amplitude \( A \) and does not vary with displacement \( x \) from the mean position.

Thus, **Statement 1 is true**.

### Step 3: Analyzing Statement 2
**Statement 2:** "The total energy of a particle executing S.H.M. is maximum at the mean position."

In S.H.M., the total energy remains constant throughout the motion. It is not correct to say that the total energy is maximum at the mean position because it does not change with position. Instead, the kinetic energy is maximum at the mean position while the potential energy is maximum at the extremes (amplitude).

Thus, **Statement 2 is false**.

### Conclusion
- **Statement 1 is true.**
- **Statement 2 is false.**

### Final Answer
The correct option is that Statement 1 is true and Statement 2 is false.

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