This problem involves a block sliding down an inclined plane, looping around a circular path, and then compressing a spring. Here’s a breakdown of how to solve each part:

Part a: Calculating Maximum Compression of the Spring

1. Energy Conservation:

   • Initially, the block has gravitational potential energy at height $h = 2.5 \, \text{m}$.
   • As it slides, friction dissipates some energy on the inclined plane and the horizontal surface $BG$.
   • After the loop, any remaining kinetic energy is used to compress the spring.

2. Calculating Initial Potential Energy: $PE = mgh = 0.6 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 2.5 \, \text{m}$

3. Frictional Work Done:

   • On Incline (AB): Use the coefficient of kinetic friction $\mu = 0.3$ along distance $AB$.
   • On Horizontal Surface (BG): Similarly, calculate work done by friction along $BG = 0.6 \, \text{m}$.

4. Loop Dynamics:

   • For the block to complete the loop, the centripetal force at the top of the loop should be considered.

5. Spring Compression:

   • After frictional losses, use energy conservation to find the compression $x$ of the spring where: $\frac{1}{2}kx^2 = \text{Remaining Kinetic Energy}$

Part b: Normal Force at Position D

1. Centripetal Force Requirement: At point $D$, calculate the normal force using centripetal acceleration requirements due to the loop’s radius $r = 0.5 \, \text{m}$.

Would you like detailed step-by-step calculations for each section? Here are some further questions for exploration:

1. How would the maximum compression change if the spring constant was different?
2. What effect would doubling the mass of the block have on the loop completion?
3. How would a change in the loop’s radius affect the required velocity to complete it?
4. How does the angle of the incline influence the frictional work done?
5. What would happen if friction were present in the loop?

Tip: In energy problems with friction, always account for each segment's work done separately.