depends on your definitions but if
x = A sin (wt-p)
u = A w cos (wt-p)
a = -A w^2 sin(wt-p) = -w^2 x
if x = 0 at t = 0
then
x = A sin (-p) = 0 and a solution is p = 0
x = A sin (wt)
u = A w cos (wt)
a = -Aw^2 sin wt = -A w^2
now u = 12 when t = 0
A w cos(0) = 12
so
A w = 12
now k = 200 N/m
F = m a = -m (Aw^2)sin w t = - k x = -k (A sin (wt))
so
w^2 = k/m ( which you probably knew :)
w^2 = 200 /3
w = 10 sqrt(2/3)
A = 12/w = 0.1 sqrt(1.5)
x = 0.1 sqrt 1.5 sin ( 10 sqrt(2/3) t)
A 3kg block is attached to an ideal spring with a
force constant k = 200N/m. The block is given
an initial velocity in the positive direction of
magnitude u = 12 m/s and no initial
displacement (x o = 0). Find (10 marks)
a. The amplitude and
b. The phase angle
c. Write an equation for the position as a
function of time
1 answer