For those wondering why cosine(ωt - Φ) was ignored: The amplitude does not depend on the position of the mass. What do you think is the amplitude at a random position x(t) during an oscillation (but not at the highest or lowest point) ? I bet you would say it is not x(t), because thats obviously not the highest or lowest point of that oscillation. So how would you find out the amplitude associated with that position? Do we know a function that only models how the amplitude changes without considering the position of the mass at that time? Yes; it is the exponential decay function of the amplitude. A(t) = A e^(-bt/2m)
Thanks so much Sir Michele Van Biezen for your online tutorials and lectures B's have helped me to Master concepts within a short range of time your is great teacher🤩💯🙏
How can I find the drag coefficient of the object using a simple harmonic motion model? I was told that it was possible to use the experiment of the damped simple harmonic motion to determine the drag coefficient of an object, but I don't know how.
last step can be shortened to multiplying frequency by time instead of converting to the period first and dividing time by period(although time saved by doing this is trivial :) )
The cosine will give you the position, velocity, or acceleration of the object at any point in time. The period is determined by the mass, spring constant, and damping factor.
+Jetshen Teoh Good question. We didn't actually ignore the cosine portion of the solution. Note how the diagram clearly shows the oscillation nature of the amplitude caused by the cosine part of the equation. But in this problem, we are interested in calculating how the amplitude of the oscillations diminish over time.
thank you for your quick reply . i have one more question : do we just use the equation for lightly damped oscillation to solve this kind of problem without finding out what kind of damping takes place before using the equation ? or the equation a(t) = A0e^(-b/2m)t is just a general equation for all case ?
do you know what the time constant is? my prof never defined it and i cant find anything online of what the time constant, tau, is and how to calculate it
In nature things grow or decay exponentially or logarithmically. If something decays from a starting value to zero logarithmically as in the diagram, a time constant is the time for the value of the decay function to drop from its initial value to (1/e) of its initial value. (1/e) = 0.368 or 36.8% of its initial value. It takes 5 such time constants for the process to come within 1% of its final value.
We didn't ignore it. This video shows how the amplitude of the oscillatory motion diminishes as a exponential decay function, while the object keeps oscillating. Note how the frequency of oscillation has been affected by the damping as well.
The only channel I always check out on every time I have something I don't understand in Physics. Thank you sir
For those wondering why cosine(ωt - Φ) was ignored:
The amplitude does not depend on the position of the mass. What do you think is the amplitude at a random position x(t) during an oscillation (but not at the highest or lowest point) ? I bet you would say it is not x(t), because thats obviously not the highest or lowest point of that oscillation. So how would you find out the amplitude associated with that position? Do we know a function that only models how the amplitude changes without considering the position of the mass at that time?
Yes; it is the exponential decay function of the amplitude. A(t) = A e^(-bt/2m)
my lord -- again this lecture is best on internet -amarjit india
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Thanks so much Sir Michele Van Biezen for your online tutorials and lectures B's have helped me to Master concepts within a short range of time your is great teacher🤩💯🙏
You are welcome. Glad you found our videos helpful.
Sir when calculating t in the very final step of putting the values into your calculator you did something wrong as the answer is 3,45 not 1,15
We just checked. The value for t is 1.15 seconds.
How can I find the drag coefficient of the object using a simple harmonic motion model? I was told that it was possible to use the experiment of the damped simple harmonic motion to determine the drag coefficient of an object, but I don't know how.
Great work sirji💜
Thanks!
Great work sir ....love from India ❤️
Thank you and welcome to the channel
last step can be shortened to multiplying frequency by time instead of converting to the period first and dividing time by period(although time saved by doing this is trivial :) )
and as always great job
Hello Mr. van Biezen. To calculate the oscillation time t, why did you calculate it without looking at the cosine part?
The cosine will give you the position, velocity, or acceleration of the object at any point in time. The period is determined by the mass, spring constant, and damping factor.
How would you calculate this if the square of the amplitude of the vibration to decay to 10^-6 versus 1/10?
Just replace the 1/10 by 1 x 10^-6
hi sir , why do we ignore the cisine part for this example ?
thank you
+Jetshen Teoh
Good question.
We didn't actually ignore the cosine portion of the solution. Note how the diagram clearly shows the oscillation nature of the amplitude caused by the cosine part of the equation.
But in this problem, we are interested in calculating how the amplitude of the oscillations diminish over time.
thank you for your quick reply . i have one more question : do we just use the equation for lightly damped oscillation to solve this kind of problem without finding out what kind of damping takes place before using the equation ? or the equation a(t) = A0e^(-b/2m)t is just a general equation for all case ?
@@jackmas1042 4 years no reply lmao
do you know what the time constant is? my prof never defined it and i cant find anything online of what the time constant, tau, is and how to calculate it
In nature things grow or decay exponentially or logarithmically. If something decays from a starting value to zero logarithmically as in the diagram, a time constant is the time for the value of the decay function to drop from its initial value to (1/e) of its initial value. (1/e) = 0.368 or 36.8% of its initial value. It takes 5 such time constants for the process to come within 1% of its final value.
Michel van Biezen thank you very much!
this is greatness thank you!
Firstly, thank you for this video. Why didn't we use "coswt" in the equation? In this case, don't we get time wrong?
The choice of cos or sin depends on the initial condition of the problem. In this case we did use cos(wt).
I dont understand how the rest of the equation with the COS (wt) was ignored ... mathematically it doesn't make sense ...
We didn't ignore it. This video shows how the amplitude of the oscillatory motion diminishes as a exponential decay function, while the object keeps oscillating. Note how the frequency of oscillation has been affected by the damping as well.
Thank you!
thank you sir
Why is b = 2?
This is a given in the problem. The 2 is made up to stage an example to work on.
I think you did something wrong during the finding t part
Thank you!!
You're welcome!