Hard Simple Harmonic Motion (1 Viewer)

[toknblackguy]

acceleration = 8x - 2x^3

when x = 2 v = 6

show the particle moves between plus and minus root 10

quesiton 2:
a particle in SMH has acceleration = -9x
EDIT: x = asin(3t + alpha)

initially the particles accceleration is 18ms-1 (possibly a typo, and may mean velocity is 18) and at t= 5pi/18, v = 12ms-1

show amplitude = 4

thanks

 

[shafqat]

for the first one, use d/dx(v^2/2) = acceleration, then integrate.
Then put v = 0 to find the boundaries of the motion

 

[currysauce]

what about the constant?

 

[toknblackguy]

shafqat
ive done that
and i get the equation x^4 - 8x^2 + 4 = 0
and that doesn't result in x = plus minus 10-^0.5

 

[shafqat]

You should end up with x^4 - 8x^2 - 20 = 0, which gives you the correct answer.

 

[toknblackguy]

You should end up with x^4 - 8x^2 - 20 = 0, which gives you the correct answer.

yep i got it
thanks shafqat - was making stupid mistake as usual

what about the second one?

 

[shafqat]

When a = 18, x = -3 (because of initial equation)
So at t = 0, -3 = asin@
Also at t = 5pi/6, v = 12.
First differentiate the expression for x: v = 3acons(3t + @)
Then sub in: 12 = 3acos(5pi/6 + @)
4 = acos(5pi/6 + @)
Now expand RHS using cos(alpha + beta) formula, sub in the value for sin@, and then you'll have an expression in acos@.
Then divide through with the expression for asin@ to eliminate a, so find @.
Then sub back in to find a.

 

[FinalFantasy]

When a = 18, x = -3 (because of initial equation)
So at t = 0, -3 = asin@
QUOTE]

he said x''=-9x
when x''=18, 18=-9x and x=-2

 

[shafqat]

My mistake. Just use that value then, the method should still work.

 

[FinalFantasy]

yap
---------------

 

[toknblackguy]

guys i tried it and my two equations are asin@ = -2
and acos@ = -10/root3

the answer doesn't come out from there

 

[toknblackguy]

no worries
i got it
thanks for all the help shafqat and FF

 

[FinalFantasy]

no need to thank me i didn't do anything lol..
shafqat is da one dat did all da work

 

[A l]

Hard Simple Harmonic Motion. It's not a very 'simple' harmonic motion is it....