A loudspeaker diaphragm is vibrating in simple harmonic motion with a frequency of 430 Hz and a maximum displacement of 0.90 mm.

what is the max speed?
what is the max acceleration?

1 answer

T = period = 1/430
for example if 0 at t = 0

y = .009 sin [2pi t/(1/430)] = .0009 sin( 860 pi t)

velocity = .0009 (860 pi) cos (860 pi t)

acceleration = -.0009 (860 pi)^2 sin(860 pi t)

the maximum of sine is 1 and the maximum of cosine is 1