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[Nikitn]

Why does the charge Q in the capacitor of a simple, series RLC circuit driven by a DC voltage-source oscillate?

Shouldn't the charge just increase? I mean, in the beginning there goes a current towards the capacitor, and the inductor is producing a counter-current. After a while the current from the battery should decrease due to the increasing resistance from the charge in the capacitor capacitor, and then the stored magnetic energy in the inductor will be transformed into a current going to the capacitor. In the end, Q reaches its maximum potential and no more current flows.

Where is the flaw in my logic? I saw an MIT lecture and there the professor took out an RLC circuit (with a DC power-supply) as an example of damped oscillators.

[knight of meh]

any system that has the ability to store energy in more than one returnable form has the ability to oscillate as it exchanges energy between the multiple forms , it will do this automatically when disturbed from rest


LCR circuits oscillate because of the interchange between LC components , magnetic and electric fields .
via an alternating current -the resistance of the circuit dissipates energy from the system as irretrievable heat so it doesn't influence oscillation frequency

when a DC source is present an LC circuit is disturbed when you switch on or off , when the circuit current will "ring" with decreasing amplitude for a period of time.
with an AC source the current is "forced" by the source , except at the resonant frequency
...

have i ever mentioned i hate math and having to put it in words? well going on the record now and saying it


i believe my memory is sound n all this but it may be mistaken although it does seem to make sense in my mind putting it very basically

[necronox]

i can help with anything related to programming and engineering.

but otherwise i have a question to anyone who can answer it, btw i am doing engineering at university, so i suppose it's not school but still not worth creating an enitre thread just for this....

A) to calculate the penetrating distance of an object inside a wall of irregular density.


scenario given to me: (they tend to give you too much information, some of it might be completely useless)
calculate the penetration of a triangular bullet of 20g whose point forms a 30 degree angle to the horizontal and is 12mm long traveling at 120 m/s (in relation to the bullet's direction) in penetrating a brick which is divided into three sections, BRICK/AIR/BRICK, each with a distance of 200mm, assume air resistance negligible and object will remain intact and complete.

the brick has a density varying from 1.6*10³ kg/m³ to 1.9*10³ kg/m³, now refer to (my book, for other values for the brick) which are:
confined compressive strength: 20 MPa
unconfined compressive strength: 20 MPa
shear strength: 20 MPa

if you need any other info let me know, i don't want a straight answer or anything like that, i just want to know how on earth am i suppose to do this or what equation or combination of, am i suppose to use?

[Alkaline Earth]

Just wanted to drop by and say thanks to all you guys. I am in pre-calculus honors this year (10th grade) and you guys helped me with algebra 1 honors all the way back in 7th...

dang.

[Logios]

@nekronox: try to make a drawing/diagram of the problem. I may not be able to solve the problem, but maybe you may spot something, in particular regarding the thickness of the brick at the particular angle of entry.
Other than that given the bullets weight and velocity you can calculate its kinetic energy to begin with.
Sorry if this was no help at all.

[Sphere]

Just wanted to drop by and say thanks to all you guys. I am in pre-calculus honors this year (10th grade) and you guys helped me with algebra 1 honors all the way back in 7th...

dang.

[Sphere]

i can help with anything related to programming and engineering.

but otherwise i have a question to anyone who can answer it, btw i am doing engineering at university, so i suppose it's not school but still not worth creating an enitre thread just for this....

A) to calculate the penetrating distance of an object inside a wall of irregular density.


scenario given to me: (they tend to give you too much information, some of it might be completely useless)
calculate the penetration of a triangular bullet of 20g whose point forms a 30 degree angle to the horizontal and is 12mm long traveling at 120 m/s (in relation to the bullet's direction) in penetrating a brick which is divided into three sections, BRICK/AIR/BRICK, each with a distance of 200mm, assume air resistance negligible and object will remain intact and complete.

the brick has a density varying from 1.6*10³ kg/m³ to 1.9*10³ kg/m³, now refer to (my book, for other values for the brick) which are:
confined compressive strength: 20 MPa
unconfined compressive strength: 20 MPa
shear strength: 20 MPa

if you need any other info let me know, i don't want a straight answer or anything like that, i just want to know how on earth am i suppose to do this or what equation or combination of, am i suppose to use?

Dear god that is mean. But to start this will definitely be a punching shear failure. If it were concrete I would calculate the punching shear strength like this ...


Were f'c is the compressive strength of your material in MPa. The Vr will be a force (kN). That is straightforward, but to get the force of the bullet you will need to know the rate of deceleration. That you'd have to estimate somehow. If it is 12mm long traveling at 120m/s, maybe it stops in approximately the time it takes to travel one bullet length?

.012/120 = t = .001s

120/t = a = 120000 m/s2

F = ma = .020kg*12000 m/s2 = 2.4 kN

Check that against the Vr you calculated before to see if you punched a cone through the first brick.

That is my best approach at least.

[necronox]

Dear god that is mean. But to start this will definitely be a punching shear failure. If it were concrete I would calculate the punching shear strength like this ...


Were f'c is the compressive strength of your material in MPa. The Vr will be a force (kN). That is straightforward, but to get the force of the bullet you will need to know the rate of deceleration. That you'd have to estimate somehow. If it is 12mm long traveling at 120m/s, maybe it stops in approximately the time it takes to travel one bullet length?

.012/120 = t = .001s

120/t = a = 120000 m/s2

F = ma = .020kg*12000 m/s2 = 2.4 kN

Check that against the Vr you calculated before to see if you punched a cone through the first brick.

That is my best approach at least.

nice, i assume you have taken backwards as positive? otherwise 120/t = -120000 m/s^2, the negative representive the deceleration, i combined this with the force applied by the bullet, but it is applied on an area that suits the following equation: pi*r^2 where r follows this equation: 1/3x+0, so, pi*(0.3333*x)^2 where x starts on 0, and let's do in increments of 1mm (thus 12 increments total), so pi*(0.3333*1)^2 = 0.349, divide force you get Netwons per / mm^2. divide that my 1000 you get N/m^2,
now using the compressive strength and all that you can get the amount of kinetic energy lost per mm, thus the speed and hence the distance travel.

am i missing somthing?

[edse]

Problem: Show that there is an M such that ||x||≤M||x||_inf for any norm.

So should I prove that the identity mapping from E to F (where E is normed space with sup-norm) is bounded in any norm or should I prove it straightforward by showing that ||x||≤M*Sup|x|? I've been thinking about the second way but can't find an inequality to begin with, ||x||≤ ?

[chriscase]

Problem: Show that there is an M such that ||x||≤M||x||_inf for any norm.

So should I prove that the identity mapping from E to F (where E is normed space with sup-norm) is bounded in any norm or should I prove it straightforward by showing that ||x||≤M*Sup|x|? I've been thinking about the second way but can't find an inequality to begin with, ||x||≤ ?

Hi edse,
I don't see a lot of problems in higher mathematics in the forum, wish I could really help but this is an area I didn't do much work in.

I assume you are in normed vector space. Since the canonical vector space/s would be R² or R³, does it make sense to work through the propositions there?

Is M assumed to be any element of the underlying field? I assume ||x|| is the norm of vector x, but I'm not clear on what is meant by ||x||_inf Could you explain what that is briefly?

[edse]

This is in an n-dimensional vector space.

||x||_inf was my attempt to write the supremum norm (aka uniform norm) = Sup|x| of all elements in the vector x.

M is actually a constant between 0 and infinity.

I can't even figure out how it would look in R². "Any norm of x is less than M times the maximum element in the vector."

In my solution I have stated that ||x||≤Mx due to some kind of linearity, don't know if this really holds.

Edit: got a little confused regarding the supremum.

[necronox]

Studying for my exams at uni, few things i can't quite get, (these are "simple" equations - to cover my 'basics' if you can call this basics. )

so: problem 1 (complex numbers):

Express (4+j)/(j(1+j)) in the form x+yj, where x and y are real

problem 2 (graphs):

Find polar & rectangular, and parametric equations of the curve: (x-4)^2+y^2=16

problem 3 (diff/implicit diff/ integration / etc...):

Given that: z=x^2 - 2x - y^2+4y+5

I) find the coordinates of any stationary point(s) and determine the nature of any such point(s)
II) If we let g = ((d^2z)/(dx^2))*((d^2z)/dy^2)) - ((d^2z)/dxdy)^2,
II.2) the surface's maximum at P if (d^2z)/(dx^2) < 0 and g>0
II.3) the sufrace's minimum at P if (d^2z)/(dx^2) > 0 and g > 0
II.4) the saddle point at P if g<0

any ideas on how? (answer not necessary - i'm just interested in how)

thanks

[Sphere]

Express (4+j)/(j(1+j)) in the form x+yj, where x and y are real

problem 2 (graphs):

Take the numerator, factor out a "j", then factor out (1+j). In Australia do you always use j as the imaginary number? I've heard that is sometimes done in the UK, but I've never seen anything other than "i" in the US.

Result:

Spoiler Alert, click show to read: 

x = -3/2
y = -5/2

[necronox]

we both use i and j, my book uses j, my assignements uses i, and exam practice uses j, previous exams uses both i and j (either one or the other), so, i'm not really sure which one we used.

mind you the convenor of our maths is somewhat... strange...

[Nikitn]

Anyone here can do this problem?

You have the two inequalities, where k is a real number;
1) |k+|sqrt(k^2-1)||<1

2) |k-|sqrt(k^2-1)|| <1

For what value of k is each of the inequalities above fulfilled?

Studying for my exams at uni, few things i can't quite get, (these are "simple" equations - to cover my 'basics' if you can call this basics. )

so: problem 1 (complex numbers):

Express (4+j)/(j(1+j)) in the form x+yj, where x and y are real

problem 2 (graphs):

Find polar & rectangular, and parametric equations of the curve: (x-4)^2+y^2=16

problem 3 (diff/implicit diff/ integration / etc...):

Given that: z=x^2 - 2x - y^2+4y+5

I) find the coordinates of any stationary point(s) and determine the nature of any such point(s)
II) If we let g = ((d^2z)/(dx^2))*((d^2z)/dy^2)) - ((d^2z)/dxdy)^2,
II.2) the surface's maximum at P if (d^2z)/(dx^2) < 0 and g>0
II.3) the sufrace's minimum at P if (d^2z)/(dx^2) > 0 and g > 0
II.4) the saddle point at P if g<0

any ideas on how? (answer not necessary - i'm just interested in how)

thanks

1) appears to be answered by sphere

2)
Polar: insert x=rcos(theta) and y=rsin(theta) into the equation, and then find r as a function of theta.
rectangular: the given curve is already defined in rectangular coordinates.
parametric equations: hint: use x=a*cos(b) +cx, y=a*sin(b) +cy....

3)
I: You want to find the point where the directional derivative in any direction is zero. To do so, the partial derivatives with regards to x and y must be zero, so just find when grad z = 0 (=> f_x= 0 and f_y = 0)
II: Use the second derivative test for local extreme values.

[Sphere]

You have the two inequalities, where k is a real number;
1) |k+|sqrt(k^2-1)||<1

2) |k-|sqrt(k^2-1)|| <1

For what value of k is each of the inequalities above fulfilled?

I get

1.) k < 0
2.) k > 0

Which do not overlap if k is a real number.

(this is helpful http://www.mathwarehouse.com/algebra...lex-number.php)

[Nikitn]

1) what if k=-1?
2) what if k=1?

In those cases you get 1<1 which is incorrect. I think for 2) k>1, and for 1) k<-1. But I have been unable to show this without using shady logic...

[Sphere]

Yeah, you are correct for 1 & -1 but there still isn't overlap. Try 1/2 or -1/2.

So...

1.) k < 0 k=/=-1
2.) k > 0 k=/=+1

Is what I got.

[Nikitn]

Yeah, I think you're right. What kind of algebra did you use to get to that result?

Edit: I just redid the problem and I now got the same as you, and I followed all the rules too. but could you show me anyway, just to be sure?

[John Doe]

I get

1.) k < 0
2.) k > 0

Which do not overlap if k is a real number.

(this is helpful http://www.mathwarehouse.com/algebra...lex-number.php)

f(k)=sqrt(k^2-1) is not defined for -1<k<1 so how do you get those answer?