# Finding the variable S using the intercept in simple harmonic motion of spring.

• Finaid
In summary, the conversation discusses an experiment to determine the value of g using simple harmonic motion and a harmonic oscillator. The individual has all the necessary variables and equations, but is struggling with finding the value of S in the T^2 equation. They have graphs and data for T^2 and x' and have calculated the value of k and g, but are unsure how to use the intercept in their calculations. They also mention that S should theoretically be about a third of the mass of the spring but are getting large values. They are seeking help with this issue.
Finaid
In an experiment to determine g using simple harmonic motion using a harmonic oscillator, a motion sensor and data logging equipment. I have all the variables but I can't figure out how to get S in the following equation:
T^2 = ((4pi^2)/k)M + ((4pi^2)/k)S ...(1)

I have a graph of T^2 (the period) vs Mass of the hanging load.
The slope is 1.863 +/- 0.016 s^2 kg^-1
The intercept is 0.006 +/- 0.001
From the above equation: k= 4pi^2/slope
=> k=21.19 +/- 0.18 kg s^-2

I also have a graph of x' (extension of spring) vs. Mass of load.
The slope is 0.421 +/- 0.034 m kg^-1
The intercept is -0.009 +/- 0.002
From the equation:
x' = (g/k)M - x1 ...(2)
g/k = slope
=> g = k(slope) = 8.92 m s^-2
and the uncertainty is +/- 0.73 m s^-2

I also know that S should theoretically be about a third of the mass of the spring (which is 0.0139kg) but i keep getting huge values ranging from 200 to 6000. I don't understand what I'm supposed to do except that it has something to do with the intercept. Any help would be much appreciated! This is just for a practical write up and isn't very important in the experiment but it's the only thing I haven't been able to work out and it's really annoying me...

And let me know if I've left out any information...

Welcome to Physics Forums.

Finaid said:
In an experiment to determine g using simple harmonic motion using a harmonic oscillator, a motion sensor and data logging equipment. I have all the variables but I can't figure out how to get S in the following equation:
T^2 = ((4pi^2)/k)M + ((4pi^2)/k)S ...(1)
If T2 and M are the variables here, then the y-intercept in this equation is _____?

I have a graph of T^2 (the period) vs Mass of the hanging load.
The slope is 1.863 +/- 0.016 s^2 kg^-1
The intercept is 0.006 +/- 0.001
From the above equation: k= 4pi^2/slope
=> k=21.19 +/- 0.18 kg s^-2

I also have a graph of x' (extension of spring) vs. Mass of load.
The slope is 0.421 +/- 0.034 m kg^-1
The intercept is -0.009 +/- 0.002
From the equation:
x' = (g/k)M - x1 ...(2)
g/k = slope
=> g = k(slope) = 8.92 m s^-2
and the uncertainty is +/- 0.73 m s^-2

I also know that S should theoretically be about a third of the mass of the spring (which is 0.0139kg) but i keep getting huge values ranging from 200 to 6000. I don't understand what I'm supposed to do except that it has something to do with the intercept. Any help would be much appreciated! This is just for a practical write up and isn't very important in the experiment but it's the only thing I haven't been able to work out and it's really annoying me...

And let me know if I've left out any information...

## What is the variable S in simple harmonic motion of a spring?

The variable S represents the displacement of the spring from its equilibrium position.

## Why is the intercept used to find the variable S?

The intercept is used because it is the point where the displacement of the spring is equal to zero, making it the equilibrium position. This allows for an accurate measurement of the displacement from this point.

## How is the intercept determined in simple harmonic motion of a spring?

The intercept is determined by measuring the distance from the equilibrium point to where the spring crosses the x-axis on a displacement vs. time graph. This point represents the maximum displacement of the spring.

## What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction of the displacement. This results in a back-and-forth motion around an equilibrium position.

## Why is the variable S important in simple harmonic motion of a spring?

The variable S is important because it represents the amplitude or maximum displacement of the spring, which is a key factor in determining the motion and energy of the system. It is also used to calculate other important quantities such as the period and frequency of the motion.

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