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#1 2021-05-07 04:28:47

mathland
Member
Registered: 2021-03-25
Posts: 443

Chain Rule

If the disk in the figure is
rotated about the vertical through an angle θ,
torsion in the wire attempts to turn the disk in the
opposite direction. The motion θ at time t
(assuming no friction or air resistance) obeys the
equation θ(t) = (pi/3)cos[(1/2)•sqrt{(2k/5}t]
where k is the coefficient of torsion of the wire.


(a) Find the angular velocity ω = dθ/dt of the disk at any time t.


(b) What is the angular velocity at t = 3?

For part (a), I gotta find the derivative using the
chain rule. As you can see, the function is not simplistic.
Can someone get me started?

For part (b), I must evaluate the derivative found in part (a)
by letting t = 3. Yes?

Thanks

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#2 2021-05-07 06:13:57

Bob
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Registered: 2010-06-20
Posts: 9,208

Re: Chain Rule

θ(t) = (pi/3)cos[(1/2)•sqrt{(2k/5}t]

Unpick the separate functions from the inside to the outside:

u = (2k/5) t

v = u^(0.5)  [ do you recognise the use of a power for a square root?]

w = v/2

θ = (pi/3)cos(w).

A four step chain is a tough one if you haven't done any two step ones first.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2021-05-07 11:22:50

mathland
Member
Registered: 2021-03-25
Posts: 443

Re: Chain Rule

Bob wrote:

θ(t) = (pi/3)cos[(1/2)•sqrt{(2k/5}t]

Unpick the separate functions from the inside to the outside:

u = (2k/5) t

v = u^(0.5)  [ do you recognise the use of a power for a square root?]

w = v/2

θ = (pi/3)cos(w).

A four step chain is a tough one if you haven't done any two step ones first.

Bob

I am not familiar with a four step chain rule process. Can you show me how this is done for study notes?

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#4 2021-05-07 11:39:27

zetafunc
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Registered: 2014-05-21
Posts: 2,352
Website

Re: Chain Rule

Hint:

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#5 2021-05-08 03:10:48

mathland
Member
Registered: 2021-03-25
Posts: 443

Re: Chain Rule

zetafunc wrote:

Hint:

I know that much. What else can you do?

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#6 2021-05-08 04:10:02

zetafunc
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Registered: 2014-05-21
Posts: 2,352
Website

Re: Chain Rule

You can calculate what each of those four terms are.

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#7 2021-05-08 10:22:23

mathland
Member
Registered: 2021-03-25
Posts: 443

Re: Chain Rule

zetafunc wrote:

You can calculate what each of those four terms are.

Sorry but I was not able to figure it out. Boy, do I miss yahoo answers.

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#8 2021-05-09 04:16:07

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,143

Re: Chain Rule

mathland wrote:
zetafunc wrote:

You can calculate what each of those four terms are.

Sorry but I was not able to figure it out. Boy, do I miss yahoo answers.

Just take the derivative of each of those functions - it's the chain rule, expressed graphically.


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#9 2021-05-09 10:37:54

mathland
Member
Registered: 2021-03-25
Posts: 443

Re: Chain Rule

Mathegocart wrote:
mathland wrote:
zetafunc wrote:

You can calculate what each of those four terms are.

Sorry but I was not able to figure it out. Boy, do I miss yahoo answers.

Just take the derivative of each of those functions - it's the chain rule, expressed graphically.

I will play with this some more. If necessary, I will return here to continue the discussion.

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