A MEMS-based accelerometer has a mass of m = 2 grams, an equivalent spring constant of k = 5 N/m, and an equivalent damping coefficient of c = 0.1 N∙s/m. Determine the natural frequency  n and the damping ratio  .

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm