An apparatus similar to the one used in lab uses an oscillating motor at one end
ID: 2252506 • Letter: A
Question
An apparatus similar to the one used in lab uses an oscillating motor at one end to vibrate a long rope with frequency f = 40 Hz and amplitude A = 0.25 m. The rope is held at constant tension by hanging a mass on the other end. The rope has mass denstiy ? = 0.02 kg/m, and tension T = 20.48 N. Assume that at t = 0 the end of the rope at x = 0 has zero y-displacement and is moving downward. What is the y-displacement of the piece of rope at x1 = 0.5 m when t = 0?
Show work please.
y1 =
An apparatus similar to the one used in lab uses an oscillating motor at one end to vibrate a long rope with frequency f = 40 Hz and amplitude A = 0.25 m. The rope is held at constant tension by hanging a mass on the other end. The rope has mass density? = 0.02 kg/m, and tension T = 20.48 N. Assume that at t = 0 the end of the rope at x = 0 has zero y-displacement and is moving downward. What is the y-displacement of the piece of rope at x1 = 0.5 m when t = 0? y1 =Explanation / Answer
v = sqrt T/0.02
= 32
lambda * f = v
lambda = 0.8
k= 2*pi/0.8 = 7.85 r/m
y = A sin (kx-wt)
y = A sin (kx) t=0
=0.25 sin(7.85*0.5 radians)
=0.25 sin(225)
= -0.177m