The phase constant depends on if you use the sine or cosine function (so the phase constant in your relative equations is not the same Φ).x(t) = Acos(wt + Φ)
x(t) = Asin(wt + Φ)
If you use cosine, then yes, it would be π/3, but should it be positive or negative?Φ = π/3, 5.24?
Use the expression with pi when you give the phase.10 = 20cosΦ
0.5 = cosΦ
Φ = π/3, 5.24?
v(t)=-Aωsin(ωt+Φ).Use the expression with pi when you give the phase.
You can decide which phase angle to use from the derivative of x(t). If x(t)=A cos (ωt+Φ) what is the sign of the derivative at t=0? What is the sigh of sin(Φ)? Which quadrant does it mean for Φ?
Infinite. But there is always a Φ with |Φ|≤π/2 so I would suggest using that one.sinΦ= 0.5. Φ=pi/6, 5pi/6
How many answers are there?
Ehild did not say that sinΦ was positive, she said that the derivative of x(t) is positive at x(0) (because the function is sloping upwards).How do you know it's positive? It's clearly negative because of the negative sign in front of amplitude. sinΦ must be negative.
This is much easier to explain than the way I perviously thought about it!The sign of the derivative of x(t) is positive at t=0 in the plot! V(t) is positive, so what is the sign of of sinΦ??