Question

(b) Find the position, velocity, and acceleration of the mass at time t = 5π/6.

Answer 1

Solution 
x(t) = 8 cos t, x(5π/6)= 8 cos(5π/6)
cos(5π/6)=cos(3π/6 + 2π/6 )=cos(π/3 +π/2)= - sin π/3  (cos (x+π/2)= -sinx)
x(t) = -8sin π/3 = - 4 .sqrt3
v(t) = -8sint = -8sin (π/3 +π/2)= -8 cosπ/3 (sin (x+π/2)= cosx)
v(t) = -8 cosπ/3 = -8/2= - 4 
a(5π/6) = - 8cost = -(- sin π/3)= 4 .sqrt3
a(5π/6) =  4 .sqrt3