The total energy of particle performing SHM depend on : -

Options

A. K, a, m
B. K, a
C. K, a, x
D. K, x

Answer

To determine the factors on which the total energy of a particle performing Simple Harmonic Motion (SHM) depends, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding SHM**:
- In SHM, a particle oscillates about an equilibrium position. The motion can be described using a spring-mass system, where the restoring force is provided by the spring.

2. **Total Energy in SHM**:
- The total mechanical energy (E) of a particle in SHM is the sum of its kinetic energy (KE) and potential energy (PE).
- The formula for total energy in SHM is given by:
\[ E = KE + PE \]

3. **Potential Energy**:
- The potential energy (PE) of a spring is given by:
\[ PE = \frac{1}{2} k x^2 \]
- Here, \( k \) is the spring constant, and \( x \) is the displacement from the equilibrium position.

4. **Maximum Amplitude**:
- At maximum amplitude (A), the displacement \( x \) is equal to \( A \), and the kinetic energy is zero. Therefore, the total energy at maximum amplitude is:
\[ E = PE = \frac{1}{2} k A^2 \]

5. **Kinetic Energy**:
- The kinetic energy (KE) of the particle can be expressed as:
\[ KE = \frac{1}{2} m v^2 \]
- However, at maximum displacement (amplitude), the velocity \( v \) is zero, so the total energy is purely potential energy at that point.

6. **Dependence of Total Energy**:
- From the equation \( E = \frac{1}{2} k A^2 \), we can see that the total energy depends on:
- The spring constant \( k \) (which measures the stiffness of the spring).
- The maximum amplitude \( A \) (the maximum displacement from the equilibrium position).

7. **Conclusion**:
- Therefore, the total energy of a particle performing SHM depends on the spring constant \( k \) and the amplitude \( A \).

### Final Answer:
The total energy of a particle performing SHM depends on the spring constant \( k \) and the amplitude \( A \).

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