Year 12s: what will be the first way you research your future options? >>

Circular Motion/Resonance

In trying to find the period of a spring-mass system, the formula for a simple pendulum (instead of the one for S-M system) was used where

T=2\pi \sqrt{l/g}

and l was the amplitude of the mass. The answer that I got was right, will the use of the wrong formula for the period work in every situation (given the right information)?

Another question. An example of resonance would be the column of air resonating in an organ pipe when driven by the air at the base creating stationary waves in the pipe. How do stationary waves relate to resonance? I know that stationary waves carry no energy, and that the amplitude varies between the nodes and antinodes being the same to an oscillating system (i think). Since resonance occurs at pi/2 phase difference, would the waves that create the stationary wave be pi/2 as well?

Reply 1

mik1a

I don't understand your questions. Why would the wrong equation give the right answer? What does "l was the amplitude of the mass" mean?

Second paragraph- can you be more precise? I don't know what is meant by, for example, "waves that create the stationary wave".

Reply 2

Daiblain

Original post by mik1a

Sorry.
'L was the Amplitude of the mass' means the amplitude of the mass-spring system, the biggest extension of the spring from the masses equilibrium point whenever it oscillates. L being l in the formula. My question is exactly the same as yours, why would the wrong formula give the right answer?

My question is basically asking how the example of the organ pipe is resonance.
By 'waves creating a stationary wave', i mean two progressive waves (waves that have a constant amplitude and carry energy) moving opposite to each other cancelling out any transfer of energy since the amplitude oscillates between 0 to max, back to 0, to min and then back to 0 (one full cycle). But im not quite sure what the two waves would come from; the organ pipe's vibrations as well as the air?

(edited 7 years ago)

Reply 3

mik1a

I can't see how that would ever work. Can you show your workings?

Reply 4

Daiblain

Original post by mik1a

I can't see how that would ever work. Can you show your workings?

Never mind, I'm an idiot. I just did the question I did a few days ago and got the same answer with the right formula.. Sorry for wasting your time.

Any help with the second question?