Anonymous

6. 2x'' + 6x - 2y = 0 (R)
y'' + 2y - 2x = 37cos(3t)

a. Show that x(t) satisfies
x'''' + 5x'' + 4x = 37cos(3t)
b. Find general soln x to above, x_p = Acos(3t) + Bsin(3t)
c. Sub x back into (R) to get y(t)
d. If both masses are x(0) = 2 meter, released, find displacement functions.

7. Suppose displace func x,y for coupled mass-spring sys ~ 6 satisfies
x'' + 5x - 2y = 0,
y'' + 2y - 2x = 3sin(2t);
x(0) = x'(0) = 0,
y(0) = 1, y'(0) = 0
Solve for x,y

8. Double pendulum swinging in vertical plane << gravity satisfies
(m1 + m2)l1^2 * theta1'' + m2*l1*theta2'' + (m1 + m2)*l1*theta1 = 0,
m2*l2^2*theta2'' + m2*l1*l2*theta1'' + m2*l2*g*theta2 = 0

for small values theta1,2. Solve system when m1 = 3, m2 = 2, l1 = l2 = 5, theta1(0) = Pi/6, theta2(0) = theta'(0) = theta2'(0) = 0.