Question

The output of a generator is given by V = V_max sin omega t. If after 0.0123 s, the output is 0.25 times V_max, what is the largest possible angular velocity of the generator? What is the next time (value of t) for which the output is 0.25 times V_max.

Answer 1

1)
V= Vmax * sin wt
at t = 0.0123 s, V=0.25*Vmax

V= Vmax * sin wt
0.25*Vmax = Vmax* sin (w*0.0123)
0.25= sin (w*0.0123)   
{sin -1 (0.25) = 14.48 degree or 0.253 rad}
0.253 rad = w*0.0123 s
w= 20.57 rad/s
This is maximum w.

2)
Output will again be 0.25 times maximum after 1 time period
Use:
w = 2*pi/T
T= 2*pi/w
= 2*pi/20.57
= 0.3 s

So time will be 0.0123 + 0.3 =0.3123 s
Answer: 0.3123 s