Question

Quick question:

I need to find the acceleration, velocity and displacement at the mid point of SMH.

So I know these are the equations:

x(t) = Asin(ωt + φ)
vx(t) = Aω cos(ωt + φ)
ax(t) = −Aω2 sin(ωt + φ)

I assume that the displacement is greatest when v=0. So I know ω=2760 A=1.60 and φ=2/pi.

So for instance when im looking for x I want to set v to 0.

vx(t) = Aω cos(ωt + φ) is it A that I will be looking to solve in this equation?

Answer 1

v(t) = Aω cos(ωt + φ)
this is zero when (ωt + φ) = pi/2, pi/2+pi, etc so you can find t when v = 0
HOWEVER
if you just want the maximum value of v it is Aω because cos is between -1 and + 1
same with max of a is Aω^2