A front-loading washing machine is mounted on a thick rubber pad that acts like a spring; the weight W=mg (with g=9.8 m/s^2) of the machine depresses the pad exactly 0.5 cm. When its rotor spins at w radians per second, the rotor exerts a vertical force F0 coswt newtons on the machine. At what speed (in revolutions per minute) will resonance vibrations occur? Neglect friction.

A harmonic motion has an amplitude of 9 mm and a frequency of 7 Hz. What is its maximum velocity in mm/s? Free Vibration of Undamped Vertical Mass: x(t)= A cosw,t+ B sin w,t or x(t) = x, cosw,t+ sin wt or Answer: 211/2: x(t) = C sin(wnt+ +) Where C = |x3 + (1 and = tan- (n)

A toddler with a mass of 14.4 kg bounces up and down in her crib. The crib mattress behaves like a light spring with force constant 1840 N/m. (a) The toddler bounces with at a frequency that allows her to reach a maximum amplitude with minimum effort. What is this frequency (in Hz)? Hz (b) The toddler now bounces high enough to lose contact with the mattress once each cycle, like a trampoline. What is the minimum amplitude of oscillation (in cm) required for this to occur? cm

Two parakeets sit on a swing with their combined center of mass 8.00 cm below the pivot. At what frequency (in Hz) do they swing?