SPRING CONSTANT- simple harmonic motion

In summary, the conversation discusses an experiment involving damped oscillations using a mass held between two springs. The speaker initially measured the spring constant by hanging masses from one vertical spring and graphing the force exerted. However, they now question the accuracy of this method and wonder if using a pulley would be more effective. Their main concern is how to calculate the effective spring constant when the mass is held between two identical springs. The expert suggests using Hooke's law and figuring it out for oneself rather than relying on an equation.
  • #1
linyen416
21
0
I'm investigating damped oscillations using a mass held between two springs.
In the experiment, I measured the spring constant using a method which now doesn't make sense.

I measured it by hanging masses from ONE vertical spring and graphing the force exerted by spring (mass times 9.8) against the elongation of spring

I think that's wrong. I think I should have used a pulley or something like this:
the glider is held between two springs. Record its equilibrium
position.
2. Attach a piece of audio tape to the glider and lay it across the “air
pulley” with a small mass suspended on the end of the tape.
3. Measure the displacement of the glider from equilibrium for 4
different hanging masses.
4. Graph the weight of the hanging mass (y axis) vs. the measured
displacement.

But I don't even understand how this method works. What does it mean by attaching a piece of tape to the glider and laying it across the 'air pulley'?

My second and main concern is that because I cannot redo the experiment, I have to somehow use the k values that I've measured using the masses hanging on the single spring. How can I fix the k values to get one that will equal the k value resulting from two springs, one on each side of the mass?

URGENT!
any input appreciated!
 
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  • #2
linyen416 said:
I measured it by hanging masses from ONE vertical spring and graphing the force exerted by spring (mass times 9.8) against the elongation of spring
That's a perfectly fine way to measure the spring constant. I assume you measured the spring constant of each spring?
My second and main concern is that because I cannot redo the experiment, I have to somehow use the k values that I've measured using the masses hanging on the single spring. How can I fix the k values to get one that will equal the k value resulting from two springs, one on each side of the mass?
How do you find the effective spring constant of the two springs together? Hint: With a spring attached to each end, is the effective spring constant greater or less than each individual spring constant?

To figure that out, imagine the mass between both springs in equilibrium. Pull it a distance X to one side. What net force (due to both springs) acts on the mass? Set that net force equal to KX, where K is the effective spring constant.
 
  • #3
I think I know what you're saying Doc. If you put two springs in seires then the effective spring constant is k times two

But my situation is where the mass is held BETWEEN the two springs.
 
  • #4
So I think one way to get the effective spring constant is to use a pulley somehow.
 
  • #5
unless there's an equation that relates the individual spring constants to the effective spring constant when the mass is held between two identical springs
 
  • #6
linyen416 said:
I think I know what you're saying Doc. If you put two springs in seires then the effective spring constant is k times two
You have it backwards.
But my situation is where the mass is held BETWEEN the two springs.
I know. :wink:
linyen416 said:
So I think one way to get the effective spring constant is to use a pulley somehow.
Huh? No need to complicate things by adding a pulley to the mix.

The way to get the effective spring constant is to do what I said in my last post. (You'll have to apply Hooke's law.)
linyen416 said:
unless there's an equation that relates the individual spring constants to the effective spring constant when the mass is held between two identical springs
Of course there is. But rather than look for such an equation in a book (you might get lucky!), just figure it out for yourself by doing what I suggested.
 

What is the definition of spring constant?

The spring constant, also known as the force constant or stiffness, is a measure of the stiffness of a spring. It is represented by the letter "k" and is defined as the force required to stretch or compress a spring by a certain distance.

How is the spring constant calculated?

The spring constant can be calculated by dividing the applied force by the displacement of the spring. It is also equal to the ratio of the elastic potential energy stored in the spring to the displacement squared.

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth between two points along a straight line. It occurs when the net force on an object is directly proportional to its displacement from its equilibrium position.

How does the spring constant affect simple harmonic motion?

The spring constant determines the frequency and amplitude of the oscillations in simple harmonic motion. A higher spring constant results in a higher frequency and smaller amplitude, while a lower spring constant results in a lower frequency and larger amplitude.

What factors can affect the spring constant?

The spring constant can be affected by the material of the spring, the dimensions of the spring, and the number of turns in the spring. It can also be affected by external factors such as temperature and the presence of other forces.

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