The force required to compress a non-standard spring as a function of displacement from equilibrium  x  is given by the equation  f(x)  =  ax2  -  bx, where  a  =  45  n/m2,  b  =  8  n/m, and the positive  x  direction is in the compression direction of the spring. write a general equation in terms of given variables for the work required to compress thai spring from equilibrium to any point xp.

The equation which define the work done by spring is w = 45 x³ - 8 x²

Explanation:

Given as :

The force is the function of distance x

I.e F(x) = a x² - b x

where

a = 45 N/m²

b = 8 N/m

Now, Wok done = Force ×displacement

I.e W = F . ds

So , W = (a x² - b x) × x

or, W = (45 x² - 8 x) × x

Or, w = 45 x³ - 8 x²

So, the equation which define the work done by spring is w = 45 x³ - 8 x²

Hence The equation which define the work done by spring is w = 45 x³ - 8 x²  Answer

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