- #1

Sarah0001

- 31

- 1

## Homework Statement

A uniform beam AOB, O being the mid point of AB, mass M, rests on three identical vertical springs with stiffness constants k1, k2 and k3 at A, O and B respectively. The bases of the springs are fixed to a horizontal platform. Determine the compression of the springs and their compressional forces in the case:

(i) k1 = k3 = k and k2 = 2k

(ii) k1 = k, k2 = 2k and k3 = 3k

**2.**

The use of Hookes law is only of need here and the rods weight for the first part. The second part additionally requires the use moments which I am confused on as well as the relationship between the relationship between the spring constant and their length of compressions relative to one another.

## The Attempt at a Solution

The assumption for the first scenario is that the compression (x) is the same for k2 as it is for k1 and k3. The markscheme makes indication this this is due to the fact that the system of rod and the three springs are symmetrical, hence compression for the middle spring must be the same as the other two.

I can understand this and which I have done.

for part (ii) I am confused the relationship between the length of the compression between the three springs:

Assume spring K3 length compressed by X

K2 " " X + B

K3 " " X+2B

Aswell as the use of moments on this question seen in the uploaded image (solution)

[/B]