Simple harmonic motion dash in equation

In summary, the '-' sign in the equation means that the component of the centripetal acceleration is negative, which is why the equation has a negative sign. This equation is related to simple harmonic motion, and has something to do with circular motion.
  • #1
chense
5
0
Why is there a '-' sign in the equation

a= -w.w.y

where a is the centripetal acceleration , w is the angular velocity and y is the displacement[?]
 
Physics news on Phys.org
  • #2
a= -w.w.y

'-' sign is there because here 'a' is component of acceleration in the radial direction which is normally taken positive outwards.As the centripetal acceleration is towards the center its component along radial direction is negative,hence the negative sign ('w' and 'y' are positive in the above equation,'w' being the magnitude of angular velocity and 'y' being the magnitude of distance from the axis of rotation)

cheers :smile:
 
  • #3
Originally posted by teddy
a= -w.w.y

'-' sign is there because here 'a' is component of acceleration in the radial direction which is normally taken positive outwards.As the centripetal acceleration is towards the center its component along radial direction is negative,hence the negative sign ('w' and 'y' are positive in the above equation,'w' being the magnitude of angular velocity and 'y' being the magnitude of distance from the axis of rotation)

cheers :smile:

Chense,

Can you just clarify what you do mean here - are you talking about circular motion, in which case teddy is right. But normally one would use 'r' for the radial distance - while you used 'y' and called it 'displacement'. Which makes me think you might mean 'amplitude' of an oscillation.

Cheers,

Ron.
 
  • #4
If there wasn't a negative sign, then if it is moving forwards at a point w>0, then it will always move forwards, with increasing velocity.

Not exactly the motion of an oscillator.
 
  • #5
Originally posted by plus
If there wasn't a negative sign, then if it is moving forwards at a point w>0, then it will always move forwards, with increasing velocity.

Not exactly the motion of an oscillator.

My point exactly - which is why I'd like chense to clarify these terms.

Cheers,

ron.
 
  • #6
Actually, the equation I mentioned is related to simple harmonic motion, but it also has some sort of connection with circular motion. (According to the tutor who gave me the equation he used the theory behind circular motion to analyse simple harmonic motion.)
 
  • #7
Originally posted by chense
Actually, the equation I mentioned is related to simple harmonic motion, but it also has some sort of connection with circular motion. (According to the tutor who gave me the equation he used the theory behind circular motion to analyse simple harmonic motion.)

Got you now!

Think of the particle moving in a circular track of radius r at constant angular velocity w. Now imagine looking at the track from the side - the particle (or, more correctly, its projection) will oscillate up and down. Let's say that the instantaneous distance of the particle above or below the central axis is y. The maximum value of y will be r, which is the amplitude of the SHM.

The equation for y is:

y = r sin w.t

Differentiating twice gets you the acceleration:

a = - r.w.w sin w.t = - w.w.y

Mathematically, that's where the minus comes from. As 'plus' mentioned, its physical significance is that as the particle gets further from y = 0, then it DEcelerates (because of the minus) and comes back again.

Cheers,

Ron.
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, with its displacement from the equilibrium point following a sinusoidal pattern.

2. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A*sin(ωt + φ), where x is the displacement from the equilibrium point, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase angle.

3. How is the period of simple harmonic motion related to its frequency?

The period T of simple harmonic motion is the time it takes for one complete cycle of oscillation. It is related to the frequency f by the equation T = 1/f.

4. What is the role of the spring constant in simple harmonic motion?

The spring constant k determines the strength of the restoring force that brings an object back to its equilibrium position. A higher spring constant results in a smaller amplitude and shorter period of oscillation.

5. Can simple harmonic motion occur in other systems besides a mass-spring system?

Yes, simple harmonic motion can occur in various systems, such as a pendulum, a vibrating string, or an electric circuit with an oscillating current. As long as there is a restoring force that is proportional to the displacement from equilibrium, the system can exhibit simple harmonic motion.

Similar threads

Replies
1
Views
378
Replies
21
Views
1K
Replies
8
Views
1K
Replies
4
Views
1K
  • Mechanics
Replies
5
Views
9K
Replies
11
Views
12K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
788
  • Advanced Physics Homework Help
Replies
6
Views
228
Replies
3
Views
4K
Back
Top