 #1
Max Loo Pin Mok
 5
 7
 TL;DR Summary

About the massspring system.
Can we derive one equation of motion from another?
In chapter 3 of Vibrations and Waves by French, there is a description about the equations of motion of a massspring system. It was written as shown in the attached picture:
Here, m is the mass on the spring, k is the spring constant, x is the extension of the spring, and t is time. My problem is about figuring out how equation (31) becomes equation (32)? I tried to differentiate 1/2 m(dx/dt)2:
I got an extra dt/dx which is not there in equation (31). Is my working wrong or is there another way of understanding what is in the textbook: "The second is, of course, the result of integrating the first with respect to the displacement x ..."?
Here, m is the mass on the spring, k is the spring constant, x is the extension of the spring, and t is time. My problem is about figuring out how equation (31) becomes equation (32)? I tried to differentiate 1/2 m(dx/dt)2:
I got an extra dt/dx which is not there in equation (31). Is my working wrong or is there another way of understanding what is in the textbook: "The second is, of course, the result of integrating the first with respect to the displacement x ..."?