X = 5 sin 2π*t U(t) - ? A(t) - ?

Question

X = 5 sin 2π*t

U(t) - ?
A(t) - ?

Answer 1

X = 5 * sin (2*π*t)
x' = v(t) = (5 * sin (2*π*t))' = 5 * 2 * π * cos (2*π*t)
v(t) = 10*π*cos (2*π*t)
x'' = a(t) = (5 * sin (2*π*t))'' = (10*π*cos (2*π*t))' = - 10*π * 2*π * sin (2*π*t)
a(t) = - 20*π² * sin (2*π*t)