Physics 16 Simple Harmonic Motion (6 of 19) Trig Equations w/ Phase Angle
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- เผยแพร่เมื่อ 10 ก.ย. 2024
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In this video I will explain how the phase angle affect the trig equations of the simple harmonic motion.
Next video can be seen at:
• Physics 16 Simple Har...
really helpful even after 6 years.......thank you so much
So far I have watched your videos on torque and now Simple harmonic motion. Thankyou so, I am able to follow your lessons extremely well, especially since last semester and this semester are online (corona virus).
good lesson for pupils) that remainds me the school time
The best teacher ever
Thank You!
I tried to solve a Duffing eq. of ẍ + x^3 = f and for the input i used F*sin(wt+phi) , then I got zero phase angle , how can I interpret this please ? i mean why the phase is zero in this case ? is it because there was no damping? thanks
The phase angle is simply a result of the initial conditions and not an outflow of the finding the solution. It only depends on where the object is at t = 0
Hi sir, I don't understand why the x(t)=A cos (wt-pi/2) need to put negative sign?
Also the x(t)=A cos (wt+pi/2) why need to put positive sign?
Thank you:)
Just like with algebra y = (x - 2)^2 moves the graph y = x^2 to the right 2 units and y = (x + 2)^2 moves the graph y = x^2 to the left 2 units. In trigonometry (wt-pi/2) moves the graph to the right 1/4 of a cycle (pi/2 = 90 degrees = 1/4 of a circle)
Thank you sir! Your teaching is very good and help me understand very clearly👍💪
keep on doing the best job , you are amazing big brue
umm, how come in the 3rd part ...X= a cos(wt+pi/2) can lead to that graph... I mean we just have to add pi/2 angle
so if in 2nd case we are decreasing the angle by pi/2 it comes to origin...but in 3rd case??? I am a bit confused..please explain
Thank you
You are welcome.
awesome, thanks for the great work
can you elaborate on the significance of phase angle such as comparison of two simple harmonic motions having the same/different phase angle and/ or frequency and amplitude
Usually the phase angle is used to denote the initial condition at time = 0. If the object is at maximum amplitude (in the positive direction) then we use the cos function (cos wt), but if the object is an eight of a cycle past that point at t = 0, we use the function cos(wt + pi/4)
Amazing! Thank you!!
You're so welcome!
Very helpful. Thank you so much! :D
@Michel Van Biezen so the phase angle does not in any way tells the angular distance the object has move? Its only purpose is to fix the initial condition i.e. position of the object at t=o?
The phase angle is indeed there to indicate at what portion (phase) of the oscillation the object is at the time where t = 0. But then given another time, we can calculate its position and you will have to include the phase angle to obtain the correct answer.
@@MichelvanBiezen I can't thank you enough
Hi,
That was a very good explanation of phase angle. I have a question. How to decide if we have x(t)= A cos (wt-pi/2) it moves the equation to the right and if we have x(t)= A cos (wt+pi/2) it moves equation to the left? Could you please elaborate on that?
The best way to find out for yourself is to plug in some values for t and see how x changes. Take a look at this video to give you a better idea how that works. PreCalculus 3: Graphing Polynomial & Rational Fcts (1 of 29) Parabola - General Graphing Rules th-cam.com/video/i2JM-h_snxQ/w-d-xo.html
Thank you so much for your prompt reply. I will look in to video suggested by you. Your videos are really easy to understand and clears basic concepts. Do you have any videos on vibration topics like free oscilation, damped free oscilation, forced oscilation, forced oscillation, resonance, modal analysis? Please let me know.
Why is it lagging in (wt-phi), it says in my book
TOP G
Thank you. 🙂
y2 = A sin (2πx/L) sin2ωt ...how to manipulate this shm equation to get a single sin or cos function ???
actually, the question is:
The ends of stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is y1 = Asin(πx / L)sinωt and energy is E1. and in another experiment, its displacement is y2 = A sin (2πx/L) sin2ωt and energy is E2, Then:-
(1)
E2 = E1
(2)
E2 = 2E1
(3)
E2 = 4E1
(4)
E2 = 16E1
I just want to know that how can we use sin and cos in springs? Where do they form angles?
We use cosine and sine for much more than just finding angles. Any periodic oscillating function such as current behavior in circuits and yes, objects oscillating at the end of a spring can be described using sine and cosine.
can u tell me the derivation of x=acos(wt)
Assuming that a is a constant, then the derivative of a cos(wt) with respect to t = -aw sin(wt)
derivative of x will the function of velocity v(x)=-wAsin(wt) and second derivative of x will be acceleration a(x) = -w^2Acos(wt)
I find this part of physics specially confusing because in calculus the period of a trigonometric function is the length of the interval that repeats itself through out the function domain. In physics however the period is the time that it takes to complete one oscillation. So when you say that pi/2 is a quarter of the period it gets confusing.
But how do you know there will be a phase angle? Questions never tell you directly :( Can you help?
Update, I figured it out lmao its pretty easy now I that I think about it hah
It depends on the initial position of the mass when t = 0, and which function you use (sin or cos). If the mass is at the maximum position x = A and you use the cos function, then there will not be a phase angle.