Spring Pendulum Consider A Pendulum Made Of A Spring With A Mass M On The End See Figure Below The Spring Is Arranged 1 (27.57 KiB) Viewed 10 times
Spring Pendulum Consider A Pendulum Made Of A Spring With A Mass M On The End See Figure Below The Spring Is Arranged 2 (46.31 KiB) Viewed 10 times
Spring Pendulum Consider A Pendulum Made Of A Spring With A Mass M On The End See Figure Below The Spring Is Arranged 3 (40.76 KiB) Viewed 10 times
Spring pendulum Consider a pendulum made of a spring with a mass m on the end (see figure below). The spring is arranged to lie in a straight line (which we can arrange by, say, wrapping the spring around a rigid massless rod). The equilibrium length of the spring is €. Let the spring have length & + x(t), and let its angle with the vertical be et). Assuming that the motion takes place in a vertical plane, find the equations of motion for x and . Potential Energy Reference 1+x keeeeeeeee m
One of the obtained Euler-Lagrange equations for the generalized coordinates of the motion for the spring pendulum is: m(1 + x)ë + 2mx = -mg sin e m<l + x)ö + 2mx) = -mg sin 0 O. O m(I + x)Ö + 2mxó mg sino m(1 + x) 4 mi) = -mg sin 0
The other Euler-Lagrange equations for the generalized coordinates of the motion for the spring pendulum is: mx = m(I + x)2 + mgcose mx = m(I + x)2 + mgcose - kx O O mx mx = m(I + x) 02 - kx m2 + x) + mycose - kx -
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!