Q:

7.1 (a) The undamped m, k moon-landing vehicle shown in Figure 7.19(a) descends to the lunar surface at a constant descent velocity V. Write the expression for the harmonic motion of the mass m after initial contact with the lunar surface, time zero. Let g be the lunar acceleration of gravity.

Figure 7.19: (a) Lunar lander descending at constant velocity. (b) Measuring muzzle velocity.

(b) Consider the single-DOF, undamped M, K system shown in Figure 7.19(b). At time zero, the system is impacted by a bullet of mass m traveling a short distance through air at a constant velocity v. With the constant quantities m, M, K, and U ( U being the deflection amplitude of the vibrating target plus imbedded bullet) being measured directly, calculate the (muzzle) velocity of the bullet, v. Could a pendulum impacted at its center of mass serve as another means of determining muzzle velocity?

(c) Consider the three-DOF pendulum system shown in Figure 2.15, for Exercise 2.4. From Examples 5.1 and 5.4, the natural frequencies and mode shapes of this system are

For initial conditions of zero initial velocity, and zero initial deflection but for a initial angular deflection of 0.1 rad for the right-hand pendulum, calculate the deflections of all three pendulums, and plot the time history of the middle pendulum for the time interval (0, 4 ?/ ).

(d)