For the spring assemblage shown below, the stiffness of elements $1$ and $2$ is $100,000\frac{N}{m}$ each. Node $3$ undergos a

displacement of $20$ mm $,$ as is shown, which is caused by some force applied as $F_3.$ Use the direct stiffness method

to:

a$)$ Determine the displacement of node $2.$

b$)$ Determine the forces in each element.

c$)$ Determine force $F_3($and also show that this value determined is sensible$).$