An 8-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. assume that the spring constant is 40 n/m and the damping constant is 3 n-sec/m. at time t = 0, an external force of 2sin2tcos2t n is applied to the system. determine the amplitude and frequency of the steady-state solution.

An alpha particle with kinetic energy 12.5 mev makes a collision with lead nucleus, but it is not "aimed" at the center of the lead nucleus, and has an initial nonzero angular momentum (with respect to the stationary lead nucleus) of magnitude l = p0 b, where p0 is the magnitude of the initial momentum of the alpha particle and b=1.40×10−12 m. (assume that the lead nucleus remains stationary and that it may be treated as a point charge. the atomic number of lead is 82. the alpha particle is a helium nucleus, with atomic number 2.) what is the distance of closest approach?