A spring has a force law of F=-200x-75x^3. Calculate the work done to compress t

Question

A spring has a force law of F=-200x-75x^3.
Calculate the work done to compress the spring by 1.5 cm fromequilibrium. Calculate the work done to stretch the springby 0.75 cm from equilibrium. I know that I have to integrate it but I am not sure if thereis something else that I have to do? A spring has a force law of F=-200x-75x^3.
Calculate the work done to compress the spring by 1.5 cm fromequilibrium. Calculate the work done to stretch the springby 0.75 cm from equilibrium. I know that I have to integrate it but I am not sure if thereis something else that I have to do?

Explanation / Answer

Given F=-200x-75x^3 (a). work done to compress the spring by 1.5 cm fromequilibrium W = integral F dx                                                                                                        = -200 ( x ^ 2 / 2 ) -75 ( x ^ 4 / 4 )                                                                                                         = -100 x ^2 - 18.75 x ^ 4 substtue x = 1.5 cm = 0.015 m   we get , W = -0.0225 - 9.492 * 10 ^ -7 (b). the work done to stretch the spring by 0.75 cmfrom equilibrium is W ' = integral F dx                                                                                                        = -200 ( x ^ 2 / 2 ) -75 ( x ^ 4 / 4 )                                                                                                         = -100 x ^2 - 18.75 x ^ 4 substtue x = 0.75 cm = 75 * 10 ^ -4 m we getanswer                                                                                                        = -200 ( x ^ 2 / 2 ) -75 ( x ^ 4 / 4 )                                                                                                         = -100 x ^2 - 18.75 x ^ 4 substtue x = 0.75 cm = 75 * 10 ^ -4 m we getanswer

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