Build me a computer program ( on Matlab) to design a spring-mass system

Job ID: 32625798

Budget: $50 – $60 USD

I am working part-time in a small start-up designing wide variety of mechanical products. For the project I work, I need to examine a spring-mass system.

What I expect from freelancer of this project:
Derive an expression for natural frequency of the system,
Develop a computer program to design a spring such that its cost is minimum, ( The computer program should read the inputs from an input file or within the program and find the design values without user intervention through iterations.)

I need following 3 documents for this project to be completed:
Matlab file consisting code(.m)
Output file(.txt)
Project file including hand calculations, explanations step by step(.pdf)

Showing iterations in this project is mandatory.