Question

1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (assume the pendulum is at its rest position at t=0).

Answer 1

Make a situation diagram where you have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the pendulum) and a vertical leg of 49 cm
so we would get
cosØ - 49/50 = .98
then Ø = .20033.. (I stored that in my calculator to keep accuracy)

so we have
(1/4)sin(πt/2) = .20033..
sin (πt/2) = .801339...
πt/2 = .9295...
t = .5917577 or π - .59175.. = 2.5498...

the pendulum will be 1 cm above its rest position at
t = appr .59 seconds or at t = appr 2.55 seconds

Answer 2

my first equation should have been

cosØ = 49/50 = .98

Answer 3

The second answer is wrong it should be 3.41seconds instead of 2.55s