How can I calculate Spring Deflection?

Question

If I have a spring of a certain spring rate k, mounted on an angle theta, measured from the horizontal, then with a vertical force F applied at the top of the spring directly downwards, how would I calculate my spring deflection?

I have been at this problem for a suspension system and yes, I am aware of motion ratios involved. I used Race Car Vehicle Dynamics by Miliken & Miliken however the spring rates I found using the method in the book were too soft for application. So I am back to the basics of springs, spring stiffness and deflection. Your help is much appreciated!

Answer 1

The solution of your question is based on the simple Hooke's law:

F = k* X or  X = F/k

X would be deflection, F = force, and k would be sppring rate.

Since you already know k, all you have to do is to calculate the actual force that is working on the spring. This can be solved by simple trigonometry and a basic knowledge of vectors. Use either sine or cosines value of theta and multiply it with F to get the value of force actually working on the spring.

Answer 2

You need to convert your vertical force into the components normal and tangential to the spring.  Then, you can use your spring rate with the spring normal force to determine the spring deflection.