Summary:: Hello, my question asks if the complex exponential equation 4e^(-j) is equal to 4 ∠-180°. I tried to use polar/rectangular conversions: a+bj=c∠θ with c=(√a^2 +b^2) and θ=tan^(-1)[b/a]
4e^(-j)=4 ∠-180°
c=4, 4=(√a^2 +b^2)
solving for a : a=(√16-b^2)
θ=tan^(-1)[b/a]= -1
b/(√16-b^2)=...
angular frequency= 50 rad/s= 2*pi*frequency
frequency= 7.96 Hz
k=2*pi/wavelength
k=2*pi/(2*1.6m) = 1.96
velocity=angular frequency/ k
velocity=50/ 1.96 = 25.5 m/s
For some reason this velocity is wrong
wavelength of string= 2*L
wavelength of string=2*0.70m= 1.4m
velocity of string= frequency * wavelength
velocity of string= 220Hz * 1.4m= 308 m/s
tension= (308m/s)^2 * 0.00196 kg/m =186N
Is the tension correct?
sorry about the mistake.
total moment of inertia= 2.03*10^(-3) kgm^2
torque= 5.2 * 0.01 = 5.2 E-2
angular acceleration = (5.2 E-2)/ (2.03E-3)= 25.6 rad/s^2
I don't know how to solve for the time.