27. The piston A moves vertically between two smooth walls. If the spring has a stiffness of . Determine the distribution of the stretch of the spring if it is subjected to a normally distributed force P ~ N(10, 0.1²) lb. The weight of the block is W ~ N(5, 0.05²) lb, and P and W are independent. Assuming the weights of rod and piston are negligible.

Solution

Also, we have

Therefore, we can obtain,

Ans.