A student extends then releases a mass attached to a spring. A graph of the mass's displacement over time is shown below. Displacement (cm) 5- 4- 3 2+ 1- -2+ -3 -4- -5- 1 2 3 4 What is the period of the oscillation? 5 6 7 Time (s) 8

1) Is it possible to prescribe the velocity v0, so that the pendulum keeps rotating with alpha = pi/2 Explain clearly why?  Given: L, g, and m. 2) After transient motion, the pendulum settles at steady state rotation atalpha = pi/3. Find the initial velocity v0. Given: L, g, m, sin(pi/3) = (squareroot(3)/2), cos(pi/3) = (1/2). [Hint: Use the conservation of energy and the 2nd Newton’s law.]

Break down how got the answer simply? For period what is as?

A single degree-of-freedom linear elastic structure was subjected to a series of harmonic excitations, one at a time. The excitations had the same forcing magnitude but different forcing frequency. Forcing frequencies and observed peak steady-state displacements are shown in the graph below. Find the natural period and damping ratio of the structure. Displacement (mm) 60 50 40 30 20 10 0 0 1 2 . 3 4 Forcing frequency, f [Hz] 5 4. 6 7