Passage IV) Angular frequency in SHM is given by `omega=sqrt(k/m)`. Maximum acceleration in SHM is `omega^(2)` A and maximum value of friction between two bodies in contact is `muN`, where N is the normal reaction between the bodies.
Now the value of k, the force constant is increased, then the maximum amplitude calcualted in above question will

Options

A. remain same
B. increase
C. decrease
D. data in insufficient

Explanation

To solve the problem, we need to analyze the relationship between the force constant \( k \) and the maximum amplitude \( A \) in a simple harmonic motion (SHM) system, particularly in the context of a spring-block system on a rough surface.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a spring with a force constant \( k \) and a mass \( m \) resting on a rough surface. The frictional force is given by \( F_{\text{friction}} = \mu N \), where \( N \) is the normal force.

2. **Equilibrium Condition**:
- At equilibrium, the spring force \( F_{\text{spring}} = k \Delta x \) (where \( \Delta x \) is the displacement from the equilibrium position) is balanced by the maximum frictional force. Thus, we have:
\[ k \Delta x = \mu N \]

3. **Effect of Increasing \( k \)**:
- If the force constant \( k \) is increased, the spring force \( F_{\text{spring}} \) for a given displacement \( \Delta x \) will also increase. This means that the system can exert a greater force for the same displacement.

4. **Acceleration in SHM**:
- The maximum acceleration \( a_{\text{max}} \) in SHM is given by:
\[ a_{\text{max}} = \omega^2 A \]
- Where \( \omega = \sqrt{\frac{k}{m}} \). If \( k \) increases, \( \omega \) increases, leading to an increase in maximum acceleration.

5. **Relation to Amplitude**:
- Since the net force acting on the block increases with an increase in \( k \), the block will be displaced further from its mean position when pulled. This means that the maximum amplitude \( A \) will also increase.

6. **Conclusion**:
- Therefore, if the value of \( k \) (the force constant) is increased, the maximum amplitude \( A \) will also increase.

### Final Answer:
If the value of \( k \) is increased, then the maximum amplitude calculated will increase.