Question

2. In class we considered a mass m connected to a pair of identical springs with spring constant k. One spring is connected to the left side of m and the other is connected to the right side. Initially, the springs are at their equilibrium lengths ro and the two springs and the centre of m are all aligned with the r-axis. The mass is on a frictionless horizontal surface. The ry-plane is horizontal. m4 co . In class, we found that if the mass was displaced in the y-direction and then released, we would get an equation of motion у ~ _ay3, where a k/ (mz8). To find y(t) and y(t), we had to resort to numerical methods. (a) Although mumerical methods were required to find y(t) and j(t), we can solve for the dependence of v on y algebraically. Use an energy analysis to determine an exact expression for v(y). Assume that the mass is released from rest when y =-A (as in the top figure). Your expression for v(y) should be in terms of k, m, xo, A, and y. (b) Show that when A, y < to: v(y) 2mr2 0

Answer 1