This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ME201 Advanced Dynamics (Fall 2007) Midterm Solution ( 100 pts ) Consider the system shown in the figure. Planar pendulum (no gravity) of mass m is free to rotate around the point O by 360 : The mass is connected to point O by a massless inextensible bar of length l . The mass is also attached to a massless linear spring of constant stiffness k and equilibrium length seq. The spring is attached to the slider B that is free to slide on the bar A: The spring always stays parallel to the (0; h ) axis. There is no friction. The system will be studied in cylindrical coordinates rthe radius measured from O and the angle measured from the vertical axis passing through O in the counterclockwise direction, as shown in the figure. Figure 1: Phase space: m = 10 ,L = 1 ,h = 5 ,s = 0 . 1 ,k = 1 A. 10 pts Derive the Newtons equation of motion for the mass m for both the radial direction r and the tangential direction : Recall that the radial acceleration and tangential acceleration are given by a r = r r 2 , a = r + 2 r Newtons equations of motion are: m a r = m r r 2 = T + k ( h r cos  s eq )cos m a = m r + 2 r = k ( h r cos  s eq )sin Where T is tension in the rod. B. 10 pts Rewrite the equations as a system of first order ordinary differential equations....
View
Full
Document
 Fall '08
 Mezic,I

Click to edit the document details