2. A body weighing 25 lb is suspended from a spring of constant k 160 lb /ft. At time t 0, it has a downward velocity of 2 ft/sec as it passes through the position of static equilibrium. Determine (a) the system period and (b) the maximum acceleration attained by the mass.

3. Figure 3 shows a system consisting of wedge A and block B connected by an inextensible cable that runs around three pulleys. The mass of A is 12 kg and the mass of B is 3 kg. Due to the application of the constant force P = 40 N, wedge A moves to the right causing block B to move up on the wedge. The friction between the wedge A and the horizontal surface is negligible. The kinetic coefficient of friction between A and B is μ = 0.25. If the system is originally at rest (before P was applied), determine the accelerations of wedge A and block B immediately after P is applied. Also, calculate the tension in the cable. Ans.: a=0.22 m/s² <; 20.3 N B A 30° P=40 N Figure 3

Q4. A two-degree-of-freedom model consisting of two masses connected in series by two springs is shown in the figure below. The physical parameters have the values m, = 8 kg, m, = 2 kg, k, = 20 N/m, and k2 = 30 N/m. X1 X2 m1 m2 k1 k2 (A) Write down the equation of motion for mass m, (B) Write down the equation of motion for mass m, Calculate the first (larger) natural frequency of the system (D) Calculate the second (smaller) natural frequency of the system

6. A 12 lb. weight stretches a spring 2 feet. The mass-spring system is immersed in a medium offering resistance that is numerically equal to one quarter of the instantaneous velocity. The weight is released from a point 1 foot below equilibrium. Find its position at any future time.