help with M3 S.H.M. Watch

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im37
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#1
Report Thread starter 13 years ago
#1
In the equation x=acoswt or x=asinwt,
x in the distance between the oscillation centre & how long it moved.... But in some questions, x might appear as -ve...

This makes me feel confusing as I dunno how x become +ve or -ve??? is it based on the position of the oscillation centre??

Grateful if anyone can help me out, thx!
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Christophicus
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#2
Report 13 years ago
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(Original post by im37)
In the equation x=acoswt or x=asinwt,
x in the distance between the oscillation centre & how long it moved.... But in some questions, x might appear as -ve...

This makes me feel confusing as I dunno how x become +ve or -ve??? is it based on the position of the oscillation centre??

Grateful if anyone can help me out, thx!
x = asin(ωt)
- Particle starts at centre of oscillation O (x = 0 when t = 0)

x = acos(ωt)
- Particle starts at either end of oscillation (x = ±a when t = 0)

Consider a particle of mass 1kg, moving with SHM,
Period = 2π seconds = 2π/ω => ω = 2π/2π = 1
Amplitude (a) = 1m
Particle starts at far end of oscillation, at +a.

Therefore, using info above.
x = acos(ωt)
x = 1cos(1t)
x = cos(t)

So attached graph shows the movement of the particle, with x-axis (time) and y-axis (displacement)

- You can see that the particle starts at 1m from the centre of oscillation O at t = 0
- At x = 0 for the first time, t = 2π/4 ≈ 1.57 seconds (see graph - it crosses the x-axis at about 1.6 seconds so this is correct)
- When the particle passes through the centre of oscillation O, the values of y (displacement) are negative. So when it reaches the ampltiude at the other side of the oscillation, this is -a and occurs at π seconds ≈ 3.14 seconds.
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im37
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#3
Report Thread starter 13 years ago
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I start to understand that...but how to determine which direction is +ve or -ve??..... is there any example to illustrate??? thx very much for ur help
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Newton
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If the displacement of the described particle is to the left of the centre of oscillations than in general we say that it's displacement is -ve, where as if it is to the right it is +ve.

Newton.
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#5
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(Original post by im37)
I start to understand that...but how to determine which direction is +ve or -ve??..... is there any example to illustrate??? thx very much for ur help
i had major problems with that, and i found that the only way you'll get anywhere is by accepting it.

to summarise i just accepted, without question that:

take displacement as +ve in direction of increasing x; therefore acceleration and velocity are also +ve in this direction also, and they are all vector quantities. therefore when a particle is moving away from O - say from left to right, then the velocity, accel and displacement is +ve in this direction. However ACCELERATION is directed towards the centre at all times therefore when x is +ve, acceleration is -ve...its all in the directions.

also as acceleration is linked to force (F=ma), when force is directed towards the centre of oscillation, so to is the acceleration - don't be confused by this...it merely implies that the accelerations MAGNITUDE is towards the centre - it is sort of a scalar definition in a sense whereas SHM includes DIRECTIONS, hence all the crap about taking one direction as +ve and other as negative,

hope this helps

PK
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#6
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(Original post by im37)
In the equation x=acoswt or x=asinwt,
x in the distance between the oscillation centre & how long it moved.... But in some questions, x might appear as -ve...

This makes me feel confusing as I dunno how x become +ve or -ve??? is it based on the position of the oscillation centre??

Grateful if anyone can help me out, thx!
no as this remains same for any one system...as i said in my other post, it is all about directions...if a particle moves inwards from a point at the amplitude and you take the inward direction as being +ve, then the displacement would be negative, and the acceleration would be +ve...if you be consistent and let left to RHS be +ve then acceleration towards O would be -ve and displacement would be +ve...etc

hope this helps

as i said before...just thing of them being opposites if you get into too much trouble - its very hard to visualise...took me months to get my head around it

pk
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im37
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#7
Report Thread starter 13 years ago
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i think i've got the idea! thx for ur help~
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