Simple Harmonic Motion (1 Viewer)

[followme]

i'm having trouble with this question. plz help thanx!

a particle moving with SHM starts from rest at a distance 3m from centre of oscillation. If the period is 2pi seconds:
find the velocity and acceleration when it is 2 m from the origin.

ans: - √5 m/s , -2m/s<SUP>2</SUP>

 

[insert-username]

T = 2pi

so n = 1 (as T = 2pi/n)

The particle starts at 3 metres from the origin. Therefore a = 3.

Acceleration = -n²x

Therefore when x = 2, acceleration = -2 m/s²

(Velocity)² = n²(a² - x²)

v² = 1(9 - 4)

So v = √5 m/s


I_F

 

[followme]

thanx. but, i got to that step as well, however the book's answer for velocity is negative root 5, which confuses me.. Does it mean its travelling in another direction?? i kept having trouble with the direction for velocity in SHM u noe..

 

[hyparzero]

Whatever direction the acceleration occurs in, then velociry should be in the same direction. ie. if acceleration = - x m/s² then velocity would be - y m/s

etc. This however,does not always apply for two dimensional motion.

 

[followme]

Another sample question (with working) has similar question with the one i posted above, but with diff. numbers, that's all.

A particle is moving with SMH starts from rest at a distance 6 m from the center of oscillation. if the period is 4pi , find the velocity and acceleration when it's 3 m from the origin.

Ans (working from the textbook) :

n=0.5

v<SUP>2</SUP> =n<SUP>2</SUP> (a<SUP>2</SUP> -x<SUP>2</SUP> )
=1/4 (36-9)
v= positive root 27 over 2

a=-n<SUP>2</SUP> x
= -1/4*3
= -0.75 m/s <SUP>2</SUP>

what the??? why is v this time + ??
Our school uses LONGMAN.

 

[insert-username]

Whatever direction the acceleration occurs in, then velociry should be in the same direction. ie. if acceleration = - x m/s² then velocity would be - y m/s

etc. This however,does not always apply for two dimensional motion.

That seems wrong to me. A particle that's just past the centre of its motion in SHM can have positive velocity (assuming that we're taking this direction as positive) but negative acceleration (since it's slowing down).

In my opinion, if you stick directly to your formulas like I did (in regard to positives and negatives) you should be OK. Unless you're given more information in the question, all you can do is stick to the formulas.


I_F

 

[hyparzero]

yea, forgot to take deceleration into account... advice, dont listen to hyparzero

 

[Riviet]

advice, dont listen to hyparzero

Random BOS member: "Advice not taken. Will continue to listen to your advice."

 

[hyparzero]

Random BOS member: "Advice not taken. Will continue to listen to your advice."

Same Random BOS member: "Why is my UAI so low."