Question

12 Our treatment of the three-spring problem was incomplete because we looked only at the cosine parts of the solutions, ignoring the sines. (a) Show that the following equations are valid solutions to Equations 6.1.1 and 6.1.2 for any constants A and A2 x (t) = Al cos (V/2 t) + A2 sin (v 2 ) (b) Show that the initial conditions h(0) = (0) = 0 lead to A2-0 and therefore to the solution we used in the Explanation (Section 6.1.1). (s (c) Do Equations 6.1.9 represent a nor- mal mode of the system? (d) The three-spring problem has four ini- tial conditions: the initial position and velocity of Ball 1 and the initial posi- tion and velocity of Ball 2. What must be true of all the initial conditions for the balls to follow Equations 6.1.9?

Answer 1

dh 汽ー:@ 3 -- 21,

Dale 2 3 วา 3