help SHM :( (1 Viewer)

[hollyy.]

question 6 a) 2007 hsc

link:
http://www.boardofstudies.nsw.edu.au/hsc_exams/exam-papers-2007/pdf_doc/maths-ex1-07.pdf

i did part (i) woo.

 

[yorkstanham]

what parts do you want help with?

 

[QuLiT]

II) x double dot = -4(x-3)

there for n^2 = 4

n = 2

therre fore period = 2pi/2
= pi

iii) i would use auxilary angle method on x then differentiate

iv) let xdot = 2 and work it out

edit: should put xdot = plus or minus 2

 

[hollyy.]

II) x double dot = -4(x-3)

there for n^2 = 4

n = 2

therre fore period = 2pi/2
= pi

iii) i would use auxilary angle method on x then differentiate

iv) let xdot = 2 and work it out

edit: should put xdot = plus or minus 2

huh!?

 

[tommykins]

ii) period = 2pi/n = 2pi/2 = pi sec
ii) x' = 2sqrt3cos2t + 2sin2t = Acos(2t-@)
A = sqrt (2sqrt3² + 2²) = sqrt 16 = 4

Acos(2t-@) = 4[cos2t.cos@ + sin2tsin@]

Using 4sin@ = 2
sin@ = 1/2
@ = pi/6

Thus x' = 4cos(2t-pi/6)

iii) for 0<t<pi
4cos(2t-pi/6) = +-2
cos(2t-pi/6) = +-1/2

I'm sure you can solve it from there.

 

[QuLiT]

mighta got the name wrong, its where you change asin@ - bcos@ into Ccos( @-alpha) where alpha is the initial phase

 

[tommykins]

It is called the auxillary angle method.

 

[hollyy.]

mighta got the name wrong, its where you change asin@ - bcos@ into Ccos( @-alpha) where alpha is the initial phase

is that the thing that u can use in trig equations instead of the t method?

 

[QuLiT]

which text book do you have? il tell you the page no

 

[hollyy.]

which text book do you have? il tell you the page no

maths in focus - the purple one

 

[QuLiT]

omg the only text book i don't have lol -.- neway its near the part with general solutions of trignometric equations

 

[hollyy.]

thanks - im so screwed.

 

[QuLiT]

here:
Transformations (equations involving the sum of sin and cos / axillary angle method)

• asinx + bcosx = rsin(x+α)
• asinx - bcosx = rsin(x-α)
• acosx - bsinx = rcos(x+α)
• acosx + bsinx = rcos(x-α)

Where:

• r = √(a² + b²)
• α is in the first quadrant such that tanα = b/a

taken from the maths formula wiki thing

 

[dwarven]

bottom half of P281 in the first book. [the green one]
=]

 

[hollyy.]

here:
Transformations (equations involving the sum of sin and cos / axillary angle method)

• asinx + bcosx = rsin(x+α)
• asinx - bcosx = rsin(x-α)
• acosx - bsinx = rcos(x+α)
• acosx + bsinx = rcos(x-α)

Where:

• r = √(a² + b²)
• α is in the first quadrant such that tanα = b/a

taken from the maths formula wiki thing

your my hero
my teacher called this the R method - because theres and R in it lol.
never heard of axillary
thankyou!

 

[hollyy.]

bottom half of P281 in the first book. [the green one]
=]

thanks

 

[QuLiT]

lol np i only learnt it recently too

 

[tommykins]

回复: Re: help SHM

here:
Transformations (equations involving the sum of sin and cos / axillary angle method)

• asinx + bcosx = rsin(x+α)
• asinx - bcosx = rsin(x-α)
• acosx - bsinx = rcos(x+α)
• acosx + bsinx = rcos(x-α)

Where:

• r = √(a² + b²)
• α is in the first quadrant such that tanα = b/a

taken from the maths formula wiki thing

wow, @ is from tan@ = b/a? that's neat.

 

[QuLiT]

theres also another way you can do @ lol

you can do cos-1 (a/R)

 

[danz90]

here:
Transformations (equations involving the sum of sin and cos / axillary angle method)

• asinx + bcosx = rsin(x+α)
• asinx - bcosx = rsin(x-α)
• acosx - bsinx = rcos(x+α)
• acosx + bsinx = rcos(x-α)

Where:

• r = √(a<SUP>2</SUP> + b<SUP>2</SUP>)
• α is in the first quadrant such that tanα = b/a

taken from the maths formula wiki thing

do we actually have to remember like each transformation.. or will they always specify in an exam to which form they want you to change it to?