Did I Make a Mistake in My Spring Constant Calculation?

In summary, the goal of this conversation is to measure the spring constant of a spring and then calculate a theoretical period of the oscillation and compare the results to a real life measurement. However, the calculation of the theoretical period for 2 Newton was completely wrong. If I had set k to 91 instead of 9.1, the resulting period would have been much closer to reality.
  • #1
squashen
3
0
The goal is to measure the spring constant of a spring and then calculate a theoretical period of the oscillation and compare the results to a real life measurement.

Extension of spring A:
Neutral: 52 cm
1 N: 41 cm
2 N: 30 cm
F = kx
k = 9.1 N/m

10 oscilliations = 9.26 seconds

Calculating the theoretical period for 2 Newton:
t=2pi*sqrt(m/k)
t=2pi*sqrt(2/9.1)=2.9 which is completely wrong compared to the real life result.
If i set k to 91 instead of 9.1 the resulting period is 0.93, much closer to reality.

Have I botched up the units along the way or what have I done wrong?

I'd be very greatful for help.
 
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  • #2
squashen said:
The goal is to measure the spring constant of a spring and then calculate a theoretical period of the oscillation and compare the results to a real life measurement.

Extension of spring A:
Neutral: 52 cm
1 N: 41 cm
2 N: 30 cm
F = kx
k = 9.1 N/m

10 oscilliations = 9.26 seconds

Calculating the theoretical period for 2 Newton:
t=2pi*sqrt(m/k)
t=2pi*sqrt(2/9.1)=2.9 which is completely wrong compared to the real life result.
If i set k to 91 instead of 9.1 the resulting period is 0.93, much closer to reality.

Have I botched up the units along the way or what have I done wrong?

I'd be very greatful for help.

On the calculation of the natural frequency, what units does "m" have? What were the units of the "2" that you put into the numerator in side the square root?
 
  • #3
the unit M is in Newtons, and its for measuring the oscilliation of the spring with a spring constant of 9.2 when its weighed down with 2 Newtons
 
  • #4
I believe I´ve found a solution, by converting the unit m from Newtons to kg it looks more correct. Sorry for the inconvenience!
 
  • #5
squashen said:
the unit M is in Newtons, and its for measuring the oscilliation of the spring with a spring constant of 9.2 when its weighed down with 2 Newtons

Are you sure?

t has what units? sec ? right?

What units do you get for "t" when you use M with units of Newtons?
 
  • #6
squashen said:
I believe I´ve found a solution, by converting the unit m from Newtons to kg it looks more correct. Sorry for the inconvenience!
Yup! "m" is the mass of the bob in kg. Newtons are units for the force that the bob exerts. F = m*g

This is why it is always a good idea to work with units on your numbers. You would have seen that you got nonsense units for the period of oscillation if you had kept units of "m" and "k".
 
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FAQ: Did I Make a Mistake in My Spring Constant Calculation?

1. What is the definition of spring constant?

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

2. How is the spring constant related to SHM?

The spring constant is directly related to Simple Harmonic Motion (SHM). According to Hooke's Law, the restoring force of a spring is directly proportional to its displacement from equilibrium. This means that as the spring constant increases, the frequency and amplitude of SHM also increase.

3. How is the spring constant calculated?

The spring constant can be calculated by dividing the applied force by the displacement of the spring. This can be represented by the equation k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

4. Can the spring constant change?

Yes, the spring constant can change depending on factors such as the material and shape of the spring, as well as the temperature and stress applied to the spring. However, for an ideal spring, the spring constant remains constant.

5. How does changing the spring constant affect the period of SHM?

Changing the spring constant will affect the period of SHM. As the spring constant increases, the period decreases, meaning that the oscillations occur more quickly. This is because a higher spring constant increases the restoring force, causing the spring to oscillate with a higher frequency.

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