When responding to sound, the human eardrum vibrates about its equilibrium position. Suppose an eardrum is vibrating with an amplitude of 5.60 10-7 m and a maximum speed of 2.82 10-3 m/s.

I don't see how A and a, is given. =/

Damon, help me!!! =(

harmonic motion with w = 2 pi *frequency or 2 pi/period

y = A sin w t
dy/dt = v = A w cos w t
d^2y/dt^2 = a = -A w^2 sin wt = -w^2 y

here
v max = Aw = 2.82*10^-3
and A = 5.6*10^-7
so
w = 2 pi f = 2 pi/T = 2.82/5.6 * 10^4
= .504*10^4 = 5040 radians/s
f = 5040/2pi = 801 Hz
T = 1/f = .00125 seconds
etc etc etc

oh

max acceleration magnitude = A w^2
= 5.6*10^-7 * (5040)^2

Well, sometimes the universe likes to play hide and seek with us. Maybe A and a ran off to join a circus or something. But don't worry, I'm here to help you solve this problem without them. Let's use our imagination and pretend that A stands for "Absolutely Amazing" and a stands for "awesome". So now we have an Absolutely Amazing eardrum vibrating with an amplitude of awesome! Isn't that much more fun? Let's continue with this imaginary adventure!

In the given question, the amplitude (A) of the eardrum's vibration is given as 5.60 * 10^(-7) m, and the maximum speed (a) is given as 2.82 * 10^(-3) m/s. Both of these values are provided as part of the question statement. The amplitude represents the maximum displacement of the eardrum from its equilibrium position, while the maximum speed represents the maximum rate at which the eardrum moves back and forth.

If you are unable to locate these values in the question, you may want to re-read the question statement or look for additional information that could provide these values.