Building this graph of simple harmonic motion

In summary, the conversation is about building a graph of period squared vs. mass for simple harmonic motion and finding the slope (which is (4*pi^2)/k) to get the spring constant. They discuss how to handle uncertainty in the calculation, and the correct method is to convert the uncertainty into a percent relative uncertainty and then divide it by the constant while keeping the percent the same. The conversation ends with one person thanking the other for clarifying and correcting their interpretation of the rules.
  • #1
rambo5330
84
0

Homework Statement


Hey I'm building a graph of period squared vs. mass for simple harmonic motion
finding the slope and getting K for a spring.

since T^2 = ((4*pi^2)/k)m
the slope is (4*pi^2)/k

so I get my slope from my graph and it has an uncertainty of +- 0.2

to get K we divide (4*pi^2) by the M +-0.2

just wondering what the rule is when your dividing a contstant by a number with uncertainty what the uncertainty is in the answer.?

Homework Equations





The Attempt at a Solution


 
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  • #2


Convert your uncertainty into percent relative uncertainty. Divide by the constant keeping the percent the same. Generally you would root mean squared error, but since only one of your values has uncertainty, the uncertainty remains the same after taking the RMSE. Convert back into absolute uncertainty.
 
  • #3


so let's say my slope is 4.7 +-.2

you say I
.2/4.7 = .0426 .0426/ (4*pi^2) =.01079

(4*pi^2)/ 4.7 = 8.40

.01079 * 8.40 = 8.40 +- .09
?
 
  • #4


You shouldn't divide your uncertainty by the constant.

8.40 [tex]\pm[/tex] 4.3%=8.40[tex]\pm[/tex].4

You should follow your sig fig rules when calculating uncertainty, but you can keep a few extra digits before getting to your final uncertainty to avoid mistakes in rounding.
 
  • #5


Hey thanks a lot makes perfect sense, went over my rules again. was mis-interpretting it...
you cleared it up thanks
 

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object oscillates back and forth around its equilibrium position due to a restoring force that is proportional to its displacement. This motion is characterized by a sinusoidal graph.

How do you build a graph of simple harmonic motion?

To build a graph of simple harmonic motion, you will need to plot the displacement of the object on the y-axis and time on the x-axis. The graph will have a sinusoidal shape, with the amplitude representing the maximum displacement and the period representing the time it takes for one complete oscillation.

What factors affect the graph of simple harmonic motion?

The graph of simple harmonic motion is affected by three main factors: amplitude, frequency, and phase. The amplitude determines the maximum displacement of the object, the frequency determines the number of oscillations per unit of time, and the phase represents the starting point of the motion on the graph.

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A sin(ωt + φ), where x is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase. This equation describes the position of the object at any given time during its oscillation.

What are some real-life examples of simple harmonic motion?

Some examples of simple harmonic motion in real life include the motion of a pendulum, the vibrations of a guitar string, and the motion of a mass on a spring. These systems follow the principles of simple harmonic motion and can be represented by a sinusoidal graph.

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