Simple Harmonic Motion, memory device

In summary, to remember that ##\omega = \sqrt{\dfrac{k}{m}}## you should use the equation ω=√k/m.
  • #1
oneplusone
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What is a good way to memorize that ## \omega = \sqrt{\dfrac{k}{m}} ## ?
I always confuse it with: ## T = 2\pi \sqrt{\dfrac{m}{k}}## , and can never tell them apart. (i guess part of it is that I'm not too familiar with it yet)
 
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  • #2
Do latex with [itex]\omega = \sqrt{\dfrac{k}{m}}[/itex].
 
  • #3
hi oneplusone! :smile:

(you need to put two #s either side of your latex :wink:)
oneplusone said:
What is a good way to memorize that ##\omega = \sqrt{\dfrac{k}{m}} ## ?
I always confuse it with: ##T = 2\pi \sqrt{\dfrac{m}{k}}## , and can never tell them apart. (i guess part of it is that I'm not too familiar with it yet)

easy-peasy …

mx'' = -kx, so m/k = -x/x'' = time squared

T is time, so ##T = 2\pi \sqrt{\dfrac{m}{k}}## :wink:
 
  • #4
oneplusone said:
What is a good way to memorize that \[ \omega = \sqrt{\dfrac{k}{m}} \] ?
I always confuse it with: \( T = 2\pi \sqrt{\dfrac{m}{k}}\) , and can never tell them apart. (i guess part of it is that I'm not too familiar with it yet)

When you have two formulas and you know one of them is correct, I find the best way is often just to reason it out. Which formula makes the most sense?

Suppose [itex]\omega = \sqrt{k/m}[/itex]. That formula tells me that the oscillations are faster when k (spring stiffness) is increased and/or m (mass) is decreased.

Suppose [itex]\omega = 2\pi \sqrt{m/k}[/itex]. That formula tells me the opposite: the oscillations are faster when k is decreased and/or m is increased.

Now, which one of those makes sense? If you keep loosening the spring, what would you expect to happen? If you think about it, it should be clear that you would expect to see big sweeping oscillations which take a lot of time, and thus you would have fewer oscillations per second (i.e. lower frequency). So the first formula has to be the right one because the second formula is telling you that a weaker spring will have faster oscillations, which doesn't make sense when you think about it. The first one agrees with what makes sense.

Another trick would be to use units. Personally, I know the units of m (kg), ω (rad/s), and T (s), but I don't know the units of k. However, I do remember Hooke's law (F = -kx), so I can easily figure out that k is measured in kg/s2. From that, I can figure out that sqrt(m/k) would have units of seconds, which means ω = 2π*sqrt(m/k) is nonsense since I have frequency on one side and seconds on the other. ω = sqrt(k/m), on the other hand, works out unit-wise (there's some funny business with radians here, but at least you can see that ω = 2π*sqrt(m/k) is definitely wrong).

Maybe you were looking for some sort of mnemonic, but the methods I've described are pretty useful for all sorts of situations like this. Basically, you use what you know to fill in the gaps of stuff you don't know. I don't have an amazing memory, personally, and I quite often find myself in the situation where I only roughly remember a formula. Usually I remember what quantities are involved, but I can't remember which one's in the numerator or denominator, or I can't remember whether it's positive or negative. However, I've just learned to very quickly figure out what the correct formula is by using what I do know (units, other formulas, conceptual understanding of the physics) to see which "version" of the formula makes sense. You can almost always figure out the correct formula that way if you at least have a decent understanding of the subject.
 
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  • #5
oneplusone said:
What is a good way to memorize that ## \omega = \sqrt{\dfrac{k}{m}} ## ?
I always confuse it with: ## T = 2\pi \sqrt{\dfrac{m}{k}}## , and can never tell them apart. (i guess part of it is that I'm not too familiar with it yet)
Its real simple ω=2πf [f(frequency)=1/T]
which implies, T=2π/ω
since you already know ω=√k/m,
just substitute and you'll get the expression for T.
Just remember ω=√k/m & ω=2π/T...look up the complete derivations if your still having trouble.
 
  • #6
If you are prepared to put up with countless ∏s turning up in your calculations then you never need to deal with ω. Just remember T = 1/f (which makes sense).
'Big boys' use ω because the Maths behaves much better when you do.
I wouldn't mind betting that. after you have gone through this whole thread, you will not find it a problem, in any case. lol. (Learning by doing)
 

1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction of the displacement. This results in a motion that is repetitive and oscillatory, such as a swinging pendulum or a mass on a spring.

2. How does Simple Harmonic Motion relate to memory devices?

Memory devices, such as hard drives and memory cards, use SHM to store and retrieve data. The data is stored in the form of binary code, which is represented by a series of ones and zeros. These ones and zeros are translated into electrical signals that are recorded as magnetic or electric fields on the device's surface. When the device is accessed, the electrical signals are read and translated back into binary code, allowing the data to be retrieved.

3. What is the equation for Simple Harmonic Motion?

The equation for SHM is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency (2π divided by the period), and φ is the phase angle (determines the starting point of the motion). This equation can be used to model various types of SHM, including the motion of a mass on a spring.

4. How does the frequency of Simple Harmonic Motion affect memory devices?

The frequency of SHM can affect the read and write speeds of memory devices. Higher frequencies result in faster data transfer rates, as the device can read and write data at a faster pace. However, too high of a frequency can cause errors in the data, so a balance must be struck to ensure reliable data storage and retrieval.

5. What are some real-life examples of Simple Harmonic Motion in memory devices?

One example is the read/write head of a hard drive, which moves back and forth in a repetitive motion to read and write data on the surface of the disk. Another example is the motion of electrons in a flash memory device, where the electrons oscillate back and forth to represent the ones and zeros of binary code. In both cases, SHM is used to store and retrieve data on the memory device.

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