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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: lacoste on May 15, 2009, 11:37:04 pm

Title: lacoste's methods questions
Post by: lacoste on May 15, 2009, 11:37:04 pm: 1).

I dont get part b and d

The thickest string of a guitar (an E note) is plucked. It vibrates so that its position after
being plucked is dE = 1.5 cos 361.28t where t is the number of seconds after it is released
and d is the position in millimetres of the middle of the string above its rest position.

(a) Find, to five decimal places, the period of vibration.
(b) How many complete vibrations will occur in one second?
(c) What is the amplitude of vibration?
The next string is plucked. It vibrates so that its amplitude is 1.2 mm, and it performs
220 vibrations per second.
(d) Write down the equation of the position of the string in the form dA = A cos nt,
giving the value of n to five decimal places and A to one decimal place.

thanks!
Title: Re: lacoste's methods questions
Post by: dekoyl on May 15, 2009, 11:42:30 pm: Well after finding the period in part A, that value indicates the time it takes for one complete vibration. For part B, just do $\frac{1}{\mbox{period}}$ .

I think
Title: Re: lacoste's methods questions
Post by: lacoste on May 16, 2009, 01:50:44 pm: find x intercepts for :

y= 2cos(3x-pi/4)

working out please.

and what is the base angle?
Title: Re: lacoste's methods questions
Post by: Flaming_Arrow on May 16, 2009, 01:54:44 pm: cos(0) = pi/2, 3pi/2
Title: Re: lacoste's methods questions
Post by: TrueTears on May 16, 2009, 01:59:42 pm: $y = 2cos(3x - \frac{\pi}{4})$

Let $3x - \frac{\pi}{4} = X$ $\implies x = \frac{1}{3}(X + \frac{\pi}{4})$

$y = 2cos(X)$

$2cos(X) = 0$

$cos(X) = 0$

$X = \frac{\pi}{2} , \frac{3\pi}{2}$

$x = \frac{1}{3}(\frac{\pi}{2} + \frac{\pi}{4})$ , $\frac{1}{3}(\frac{3\pi}{2} + \frac{\pi}{4})$

$x = \frac{\pi}{4} , \frac{7\pi}{12}$

No domain is specified, you should give a general solution, if a domain is specificed, just add/minus the period ( $\frac{2\pi}{3}$ ) to get the other values.
Title: Re: lacoste's methods questions
Post by: lacoste on May 16, 2009, 02:07:07 pm: Why do we add 2pi/3?

where did you get that from?

thanks!!
Title: Re: lacoste's methods questions
Post by: TrueTears on May 16, 2009, 02:11:09 pm: period $= \frac{2\pi}{n}$ where n is the coefficient of x

$y = 2cos(3x - \frac{\pi}{4})$

3 is the coefficient of x

so the period is $\frac{2\pi}{3}$