My homework Question is:


a) Two voltages 75.sin(ωt-2pi/3) and 50.sin ωt are added together, determine the resuting voltage.

b) Then determine the first time the resulting voltage has an amplitude of 30V, given that the frequency of each of the individual waves is 25 Hz.

I get the answer "66.14sin (ωt-79.1) for part a.
However I am stuck on part b. Can anybody help me solve part b?
(I bet its easy but my mind has gone blank!)

 

Assuming that the answer you have for the sum is correct, you should be able to substitute the value 2*pi*25 in place of ω and then set the equation equal to 30 and solve for t.

hgmjr

 

I get 157.07 for 2*pi*25

I then use t=2*pi/ω to get 0.039s

But I am confused as to where the 30v comes into it?

 

My homework Question is:


a) Two voltages 75.sin(ωt-2pi/3) and 50.sin ωt are added together, determine the resuting voltage.

b) Then determine the first time the resulting voltage has an amplitude of 30V, given that the frequency of each of the individual waves is 25 Hz.

I get the answer "66.14sin (ωt-79.1) for part a.
However I am stuck on part b. Can anybody help me solve part b?
(I bet its easy but my mind has gone blank!)

The periodic nature of a sinusoidal function means that it takes on the same value at various points in time. This problem is asking you to find the value of the variable time t at which the equation takes on the value 30V for the first time. That is why you need to set the equation equal to the value 30V.

hgmjr

 

I got there in the end.
Thank you for your time and your patience.

 

I get the answer "66.14sin (ωt-79.1) for part a.

Assuming the θ values are in radians, I got 66.14 sin (ωt-1.38).
It looks like you forgot to convert degrees back to radians
(-1.38 rad = -79.1 deg)

Otherwise, if the θ values are in degrees, I get 124.95 sin(ωt-1.26)