Problem $3\mathrm{.}3$

The mass$-$spring model below is commonly used in vehicle suspension systems. The springs exert

a force that is proportional to their compression. The side springs provide additional resistance if

the weight of the object is too heavy for the center spring.

In static equilibrium, the weight must balance the spring forces as shown in the following

equations.

$x=\{\begin{array}{ccc}\frac{W}{k_1},& \text{w}\text{h}\text{e}\text{n}& W=k_{1}d\end{array}$

where

$x$ is the displacement of the platform $($m$)$

$W$ is the weight of the object $(N)$

$k_1$ is the spring constant in the center spring $(10000\frac{N}{m})$

$k_2$ is the spring constant in the side springs $(15000\frac{N}{m})$

$d$ is vertical distance to the side springs $(0\mathrm{.}1m)$

Write a function to calculate the displacement of the platform given the weight of the object

complete the following tasks:

a$)$ Define appropriate input argument$($s$)$ for the function. Assume that you will be given only

$1$ weight value $($not a vector of weight values$).$

b$)$ Calculate the displacement of the platform $x$ given the weight of the object $W$ using the

equations above.

c$)$ Define appropriate output argument$($s$)$ for the function.

In the command window:

Test Case $1$: Test the function with $W=500N.$ Check your answer with the solution below.

Test Case $2$: Test the function with two other $W$ values. One value should test each condition

above.