stupid SHM signs (1 Viewer)

[sasquatch]

For this question:

A body is vibrating in simple harmonic motion, the period being 12 seconds and the amplitude 10 cm. What is the velocity and acceleration of the body when the displacement is 6 cm.

x'² = n²(a² - x²

12=2pi/n
n = pi/6
a = 10

so when x = 6,

x'² = pi²/36(100 - 36)
x' = +/- 4pi/3 cm/s

x'' = -n²

so when x = 6

x'' = -pi²/6 cm/s²

but in the answer both the velocity and acceleration are positive. I always get screwed up with signs, what did i do wrong here?

 

[.ben]

I have the same problem

 

[vafa]

you need to think about the definition of a simple harmonic motion.

and in that definition we said that acceleration is always towards the origin. if we take the right as our positive and lef as our negative at x=6 the acceleration should be negative since it is towards origin but if we were to find acceleration at x=-6 it should have positive sign. now lets look at velocity.

we obtain equation of velocity by differentiating the equation of displacement hence where displacement is max or min then velocity is zero so when the particle is at x=6 it still has positive velocity because it is trying to reach to x=10 and it decreases velocity to get zero velocity at x=10. one its velocity is 0 then it again tries to increase the velocity by negative sing just consider the absoloute value of v and tends to go to the left hand side where it gets its max velocity at x=0. it continues to move to left and it decreases its velocity untill it reaches x=-10 and then its velocity is then 0. then again it goes to x=10 and so on...

note: when velocity is zero the sign of a indicates the direction of motion but in other than this the sign of v indicates the direction of motion.

 

[vafa]

but again you can not specify the sign of v at x=6 since it can be in x=6 at two different times in an oscillation. one with positive velocity when it is going to x=10 and the other one with negative sign when it is going to 0.

 

[vafa]

I found another interesting results and that is your period lets say is T
If x=20 in T seconds then what T will you have if x=6 or what t will you have when x=16 and that gives you the value of t.

 

[abhi_89]

I have the same problem

SHM IS THE SHITTEST TOPIC IN THE EXTENSION 1 COURSE !..and it aint very "simple" as they call it

 

[abhi_89]

For this question:

A body is vibrating in simple harmonic motion, the period being 12 seconds and the amplitude 10 cm. What is the velocity and acceleration of the body when the displacement is 6 cm.

x'² = n²(a² - x²

12=2pi/n
n = pi/6
a = 10

so when x = 6,

x'² = pi²/36(100 - 36)
x' = +/- 4pi/3 cm/s

x'' = -n²

so when x = 6

x'' = -pi²/6 cm/s²

but in the answer both the velocity and acceleration are positive. I always get screwed up with signs, what did i do wrong here?

JAMIE IS THAT YOU.. ?

 

[sasquatch]

uh huh...

anyway.. so vafa, i still dont get the point you were making with all the stuff you said... you said for the acc. if you take x = 6, then acc < 0, but if you take x = - 6, acc > 0. well i took x = 6, but from the question it states the displacement is 6m from the origin. This does not say in which direction, so yeah i dont get it then...

stupid questions..

 

[vafa]

ok i also have done this question an another alternative way but first i explain what i said already and then i attach the alternative solution
1. left indicates negative and right indicates positive
2. in simple harmonic motion acceleration is always towards origin
3. when x=6, based on the definition of shm acceleration is towards origin, to the left means sign of acceleration is negative
4. when x=-6 based on defintion of shm the acceleration is towards origin that means to the right so acceleration is positive

I hope you have understood this and this is my third alternative solution to this question:

View attachment 13609

View attachment 13610

 

[vafa]

if the question does not indicate 6m to the right or left of the origin then you need to say acceleration has negative and positive sign and then explain where each of these cases occur.

 

[vojnik]

Very nice work there Vafa, your help is very good and I applaude the effort you put into helping people.