Answer
(a) The maximum force acting on the diaphragm is $1420~N$
(b) The mechanical energy of the diaphragm is $0.128~J$
Work Step by Step
(a) We can find the maximum acceleration:
$a_m = A~\omega^2$
$a_m = A~(2\pi~f)^2$
$a_m = (1.8\times 10^{-4}~m)~(2\pi)^2~(2000~Hz)^2$
$a_m = 28,424~m/s^2$
We can find the maximum force $F_m$:
$F_m = m~a_m$
$F_m = (0.050~kg)(28,424~m/s^2)$
$F_m = 1420~N$
The maximum force acting on the diaphragm is $1420~N$
(b) We can find the mechanical energy of the diaphragm:
$E = \frac{1}{2}m~v_m^2$
$E = \frac{1}{2}m~(A~\omega)^2$
$E = \frac{1}{2}m~A^2~(2\pi~f)^2$
$E = \frac{1}{2}(0.050~kg)~(1.8\times 10^{-4}~m)^2~(2\pi)^2~(2000~Hz)^2$
$E = 0.128~J$
The mechanical energy of the diaphragm is $0.128~J$.
