Work function A spring has a restoring force given by F(x) = 25x. Let W(x)be the work required to stretch the spring from its equilibrium position (x = 0) to a variable distance x. Graph the work function. Compare the work required to stretch the spring x units from equilibrium to the work required to compress the spring x units from equilibrium.

Solution 22E Step1 Given that A spring has a restoring forcegiven by ( 5 . Let W )be the work required to stretch the spring from its equilibri m position = 0) to a variable distance x. Step2 To Find Graph the work function. Compare the work required to stretch the spring x units from equilibrium to the work required to compress the spring x units from equilibrium. Step3 A spring has a restoring force given by, F(x)=25x The work required to stretch the spring from its equilibrium position(x=0)to a variable distance is expressed as function of x given by W(x).. If the spring is stretched then distance is positive and on being compressed it is negative. Step4 The work is done in stretching the spring x units from its equilibrium position is b W=f(x) dx a x =25x dx 0 x =25 dx 0 x x2 =25 [ 2 0 x2 = 25[ 2 -0] x2 =25* 2 = 12.5x 2 Therefore, The work is done in stretching the spring x units from its equilibrium position is 2 12.5x -------------------(1) Step5 The work is done in compressing the spring x units from its equilibrium position is b W= (x) dx a x = 25x dx 0 x =25 x dx 0 x2 x =25 [ 2 0 x2 = 25[ 2-0] x2 =25* 2 2 = 12.5x Therefore, The work is done in compressing the spring x units from its equilibrium position is 2 12.5x -------------------(2) Step6 Graph for work function is Step7 From equations (1)and (2), we get that work done is equal and Positive for compressing or stretching the spring to a distance x