Consider two equal-mass carts on a horizontal, frictionless track. The carts are connected to each other by a single spring of force constant k, but are otherwise free to move freely along the track. (a) Write down the Lagrangian and find the normal frequencies of the system. Show that one of the Figure 11.20 11.26 normal frequencies is zero. (b) Find and describe the motion in the normal mode whose frequency is nonzero. (c) Do the same for the mode with zero frequency. [Hint: This one requires some thought. It isn't immediately clear what oscillations of zero frequency are. Notice that the eigenvalue equation (K w2M)a = 0 reduces to Ka = 0 in this case. Consider a solution x(t) = a f (t), where f (t) is an undetermined function of t and use the equation of motion, MX = Kx, to show that this solution represents motion of the whole system with constant velocity. Explain why this kind of motion is possible here but not in the previous examples.]

STAT 250 FEB 1, 2017 Section 2.1 David Holmes Moving Forward • After data has been collected (from an observational study or a controlled experiment), we need to identify and visualize the key features of the data. – (Ch. 2) Describe the data using visual methods (graphs). – Goal: See patterns; identify important trends and...