BF2S Forums Need help with derivatives.

SharkyMcshark wrote:

Ok I've got this....

H = 4.4 sin(0.2t) + 110    ----> at t=0 gives 110, and the max value attainable is 114.4

therefore

rate of change of height = 0.2 x (4.4 cos(0.2t))     -----> gives a rate of change of 0.2 at t=0


therefore

h(24) = 4.4 sin(4.8) + 110

=  105.617 (3 dp)

h48 = 4.4 sin (9.6) + 110

= 109.232  (3 dp)


Can I has biscuit?

1st note: If right i <3 you
2nd note: where you get the 3dp?

Ok I've got this....

H = 4.4 sin((1/22)t) + 110    ----> at t=0 gives 110, and the max value attainable is 114.4

therefore

rate of change of height = 1/22 x (4.4 cos(0.2t))     -----> gives a rate of change of 0.2 at t=0
                                    =  0.2 cos ((1/22)t)

therefore

h(24) = 4.4 sin(24/22) + 110

=  113.903 (3 dp)

h(48) = 4.4 sin (48/22) + 110

= 113.604  (3 dp)


That would be how I would approach this question (I got an A for calculus too... a year mark of 81%)
Can I has biscuit?

What I got wrong was that kt x 4.4 had to equal 0.2, and the mistake I made was just having 0.2t.

So yeah that should do it.
My bad

Liberal-Sl@yer wrote:

SharkyMcshark wrote:

Ok I've got this....

H = 4.4 sin((1/22)t) + 110    ----> at t=0 gives 110, and the max value attainable is 114.4

therefore

rate of change of height = 1/22 x (4.4 cos(0.2t))     -----> gives a rate of change of 0.2 at t=0
                                    =  0.2 cos ((1/22)t)

therefore

h(24) = 4.4 sin(24/22) + 110

=  113.903 (3 dp)

h(48) = 4.4 sin (48/22) + 110

= 113.604  (3 dp)


That would be how I would approach this question (I got an A for calculus too... a year mark of 81%)
Can I has biscuit?

What I got wrong was that kt x 4.4 had to equal 0.2, and the mistake I made was just having 0.2t.

So yeah that should do it.
My bad

Once agian what is 3dp?
Also how did you get these numbers and what do they mean because i have to actually explain this in words

OK 3dp means 3 decimal places.

The question is one of "Simple Harmonic Motion" - or at least that's how I would have done it if I'd seen this in an exam.

The idea of SHM is that the level of water oscillates around a certain point (in the case of water the average height level, which is 110 in this case)



Thats the sin graph, and it shows the oscillations around the point. sin (0) = 0, which means when t = 0 the water height is at the mean level. Also, the highest value sin(x) can take on is 1 (at 0.5xpi, 2.5 xpi etc etc). Therefore if the mean level of the water is 110, and it is at that point at t=0, therefore 0 + k = 110, k = 110

Therefore 4.4 sin ((1/22) t) + 100 is the water level.

Now, when deriving sin(kt), the derivative is kcos (kt), and as the rate of change of water level at t=0 is 0.2, and cos(0) = 1, then 4.4xk = 0.2, k = 1/22.

And then you substitute the numbers into the water height equation. t is hours right?

SharkyMcshark wrote:

Liberal-Sl@yer wrote:

SharkyMcshark wrote:

Ok I've got this....

H = 4.4 sin((1/22)t) + 110    ----> at t=0 gives 110, and the max value attainable is 114.4

therefore

rate of change of height = 1/22 x (4.4 cos(0.2t))     -----> gives a rate of change of 0.2 at t=0
                                    =  0.2 cos ((1/22)t)

therefore

h(24) = 4.4 sin(24/22) + 110

=  113.903 (3 dp)

h(48) = 4.4 sin (48/22) + 110

= 113.604  (3 dp)


That would be how I would approach this question (I got an A for calculus too... a year mark of 81%)
Can I has biscuit?

What I got wrong was that kt x 4.4 had to equal 0.2, and the mistake I made was just having 0.2t.

So yeah that should do it.
My bad

Once agian what is 3dp?
Also how did you get these numbers and what do they mean because i have to actually explain this in words

OK 3dp means 3 decimal places.

The question is one of "Simple Harmonic Motion" - or at least that's how I would have done it if I'd seen this in an exam.

The idea of SHM is that the level of water oscillates around a certain point (in the case of water the average height level, which is 110 in this case)

http://home.alltel.net/okrebs/C3-7.gif

Thats the sin graph, and it shows the oscillations around the point. sin (0) = 0, which means when t = 0 the water height is at the mean level. Also, the highest value sin(x) can take on is 1 (at 0.5xpi, 2.5 xpi etc etc). Therefore if the mean level of the water is 110, and it is at that point at t=0, therefore 0 + k = 110, k = 110

Therefore 4.4 sin ((1/22) t) + 100 is the water level.

Now, when deriving sin(kt), the derivative is kcos (kt), and as the rate of change of water level at t=0 is 0.2, and cos(0) = 1, then 4.4xk = 0.2, k = 1/22.

And then you substitute the numbers into the water height equation. t is hours right?

Wait nvm i learned SHM a fe chapters back but i didnt member it k thnx man ur a lifesaver (and not a fruity one =P)

Last edited by Liberal-Sl@yer (2007-11-26 19:36:10)

Yes. The entire portion of the height graph is concave downward, which means the derivative (rate of change) is constantly changing.

The sin function has a max value of 1. Multiplying it by 4.4 will get 4.4, and adding this to the 110 gets the peak value of 114.4.

Yw.

I think it makes the derivative of the function .2 at t=0.

SharkyMcshark wrote:

Liberal-Sl@yer wrote:

last question where does he get the 1/22?

because 1/22 x 4.4 = 0.2, which is the rate of change at t=0

yay thanks