Simple Harmonic Motion Questions (1 Viewer)

[housemouse]

1) A particle moves in simple harmonic motion. Find the period of the motion if:
the acceleration is 4m/s^2 when the particle is 2cm from the centre of the motion

2) A particle is moving in simple harmonic motion. Find the speed of the particle when it is passing through the centre of its motion given:
the amplitude is 10cm and the period is pi/2

EDIT: if you are willing to help me, could you include working out. Thank you

 

[Mountain.Dew]

1) A particle moves in simple harmonic motion. Find the period of the motion if:
the acceleration is 4m/s^2 when the particle is 2cm from the centre of the motion

2) A particle is moving in simple harmonic motion. Find the speed of the particle when it is passing through the centre of its motion given:
the amplitude is 10cm and the period is pi/2

EDIT: if you are willing to help me, could you include working out. Thank you

BIG BIG BIG NOTE: THIS METHOD IS WRONG! CORRECT METHOD AT 5TH POST!

1)
okay, using F =mrw^2 (w = omega, the angular velocity) ==> a = rw^2

so w^2 = a/r = 4/0.02 = 200 therefore w = 10sqrt2

using formulae that T = 2pi/w, we have T = 2pi/(10sqrt2) = sqrt2pi/10 seconds.

will come to question 2 later.

 

[housemouse]

Ive never seen that formula before.

 

[Mountain.Dew]

Ive never seen that formula before.

WHOOPS! BIG MISTAKE!

those formulae are 4U formulae. im so so terribly sorry about that.

 

[Mountain.Dew]

okay, heres the 3U method:

1)

acceleration is 4m/s^2 when x=-2.

so, using the formula a (or x 'double dot') = -n^2x...

sub a=4, x=-2

so 4 = -n^2 (-2) so 2=n^2, n=sqrt2

therefore, applying this to T = 2pi/n, T = 2pi/sqrt2 = sqrt2 pi

therefore the period is sqrt2pi seconds.

 

[Riviet]

WHOOPS! BIG MISTAKE!

those formulae are 4U formulae. im so so terribly sorry about that.

Just thought you might want to know that he is a 4u student.

 

[pLuvia]

Just thought you might want to know that he is a 4u student.

Yeh but he should learn by using the 3u method first

 

[housemouse]

Ive only done Complex Numbers and Curve Sketching at school for 4u and only started Conics this week.
Not up to this in 4u.
EDIT: just one question, why did you have x=-2 not x=2. In the question it doesnt state which direction.......................... or is it just to get rid of the negative ?????

 

[Mountain.Dew]

EDIT: just one question, why did you have x=-2 not x=2. In the question it doesnt state which direction.......................... or is it just to get rid of the negative ?????

remember in ur question it merely stated two cms FROM THE CENTRE. that means the particle can be at x=2 and x=-2, both are 2 cms away from centre.

and yes, i used x=-2 to get rid of the negative. it also works logically in its application in reality as well --> think of a pendulum. the acceleration is always towards the centre. when x < 0, a > 0. and vice versa.

Just thought you might want to know that he is a 4u student.

WAS a 4U student.

Yeh but he should learn by using the 3u method first

i did the answers to whatever came to my head first. naturally, the 4U methods comes to mind first.

 

[Riviet]

WAS a 4U student.

Yes, of course you were a 4u student, otherwise you wouldn't be using 4u methods.

I was actually referring to housemouse.

 

[Mountain.Dew]

Yes, of course you were a 4u student, otherwise you wouldn't be using 4u methods.

I was actually referring to housemouse.

sorry, riviet, my bad.

*repetitively bangs head on wall*