Question

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 = 65 n/m2, b = 12 n/m, and the positive x direction is in the compression direction of the spring.

Answer 1

Answer: F(x) = ax^2 - bx or F(x) = ax² - bx F(x) = 30x² - 6x â«F(x)dx = â«(30x² - 6x)dx as this is evaluated from zero to x W = 10xÂł - 3x² <===ANS W = 10(0.42Âł) - 3(0.42²) - [10(0Âł) - 3(0²)] W = 0.212 J <===ANS W = 10(0.72Âł) - 3(0.72²) - [10(0.42Âł) - 3(0.42²)] W = 1.966 J <===ANS