Simple Harmonic Motion (1 Viewer)

[Ryuu-jin-jakka]

The velocity vms-1 of a particle moving in simple harmnic motion is given by
v = root (-5 + 6x - x^2)

i) Find the two points where the particle comes to rest


iii) Determine the acceleration of the particle in terms of x

 

[L]

check the smh

 

[Uncle]

i) Find the two points where the particle comes to rest

When the particle comes to rest, that means v = 0.
v can equal zero if the inside of the square root is zero.
That means, just use the quadratic rule or whatever to find the two roots of
-5 + 6x - x² = 0
The two roots you find are the two points when this particle comes to rest.
(They must be positive and unequal)

Spoiler

When the particle is at x = 1 and x = 5

So ignore the square roots, as long as x = either of your two roots, square root of -5 + 6x - x² or not, v = 0


iii) Determine the acceleration of the particle in terms of x

kinda fading memory but you may need to use the chain rule.

dv/dt = dv/dx . dx/dt

check the smh

hahah real fuckin funny. (sarcasm)

Simple Motion Harmonic.

 

[gurmies]

sydney morning herald

 

[Aquawhite]

sydney morning herald

+1 and lmao xD

 

[Ryuu-jin-jakka]

GG exactly what i was thinking ^.^

 

[Ryuu-jin-jakka]

iii) Determine the acceleration of the particle in terms of x

kinda fading memory but you may need to use the chain rule.

dv/dt = dv/dx . dx/dt

I tried to do it but couldn't someone help me plz :S

 

[gurmies]

Accerlation = d(1/2.v^2)/dx

v^2 = -5 + 6x-x^2

1/2 . v^2 = (-5 + 6x - x^2)/2

a=d(1/2.v^2)/dx = 3-x

 

[Timothy.Siu]

The velocity vms-1 of a particle moving in simple harmnic motion is given by
v = root (-5 + 6x - x^2)

i) Find the two points where the particle comes to rest


iii) Determine the acceleration of the particle in terms of x

v^2=-5+6x-x^2
0.5v^2=0.5(-5+6x-x^2)
d(0.5v^2)/dx=0.5(6-2x)
a=3-x

 

[Ryuu-jin-jakka]

yes thank u ! ^.^

 

[Uncle]

acceleration is defined as the rate of change of velocity with respect to time. i.e. dv/dt
but you are all differentiating velocity with respect to displacement.

i cant believe maths extension 1 has taught you kids the wrong things.
fuck you guys are cunts.

 

[Drongoski]

This is same type as I solved for u earlier.



Edit

Of course for finding where particle is at rest, u can simply solve for: v^2 = 0 ==> x^2-6x+5 = 0 ==> x=1, 5