Help Needed: Deriving Expressions for Mass-Spring System

[chocofingers]

Could somebody help me in deriving the following expressions?
I can judge that the first equation is a common expression for finding Keq for a mass-spring system in series.. Can't do the rest :/ anybody please ?

Thanks in advance.

 

[Doc Al]

Show how you would derive the first equation. You'd use similar thinking for all three.

 

[chocofingers]

I don't know how to derive the first equation... If you could help me though for all the three... :)

 

[Doc Al]

You give it a try. Hint: What's the relationship between the tension in each spring?

 

[chocofingers]

Doc Al i gave it a try. I know the formulas ... tension(F) = k x e(extension) ...
so K1 e1 = K2 e2

Next what to do ?

 

[Doc Al]

I know the formulas ... tension(F) = k x e(extension) ...
so K1 e1 = K2 e2

Good! Now realize that e1 = x1 and e2 = x2 - x1.

 

[chocofingers]

what is x1 and x2 ? is x1 the extension of spring e1 ? then what is x2?

 

[chocofingers]

sorry i mean x2?

 

[Doc Al]

what is x1 and x2 ? is x1 the extension of spring e1 ? then what is x2?

I'd say (just from looking at the equation) that x1 is the displacement of the end of spring one from its unstretched position and x2 is the displacement of the right side of spring two from its unstretched position. Since the left side of spring one is fixed, x1 happens to equal the amount of stretch of spring one.