Program Requirements

Using the conservation of energy, an engineer needs to determine how much a spring is compressed to determine the effectiveness of the spring. Assuming a crate with a varying mass is dropped from a specified height, determine the value of $x($amount of spring compression$).$

The program should prompt the user to enter the height in meters $(m),$ mass of the crate in kilograms $(kg),$ and the spring constant value $(\frac{N}{m}).$ The height and mass should be greater than $0.$ The spring constant, $k,$ should be an integer, should be greater than $0,$ and should be no more than $2,500$ because a higher $k$ value would mean a higher cost. If the value entered does not meet these requirements, then the program should display the message "Invalid input" and the program should end.

Conservation of energy equation: $mgh=\frac{1}{2}k{x}^2$

Where

$h=y$ plus the distance the spring is compressed.

$g=$ gravity $(9\mathrm{.}81)$

As example with height of $5m(y)$ and mass of $4kg(m)$ :

$mg(y+x)=\frac{1}{2}(k)x^2$

$\frac{1}{2}k{x}^2-4gx-20g=0($solving the equation results in a quadratic equation$).$ Since the values of height and mass will vary, the values in the quadratic equation will change.

To assist in the engineering analysis of the other parameters, write a Java program to solve for the value of $x.$ The output should be two values. As an example, "The amount of spring compression, $x,$ is $0\mathrm{.}705$ meters and $-4\mathrm{.}326$ meters".