# Can I determine mass & spring k from graph of wave, t, a, & vectors?

• michael872940
In summary, the conversation discusses the use of Hooke's law to solve for either mass or spring constant. The possibility of using a graph of a wavelike structure to measure variables such as period, time, displacement, velocity, and acceleration is also mentioned. Gravity is not a factor in this example. Different methods of solving for mass and spring constant are suggested, such as using an equation applied to pendulums or using the equation Uel(x) = 1/2kx². However, it is noted that it is not possible to determine the actual values of k and m separately, only their ratio.
michael872940
Classical problems for hookes law generally give either mass or spring constant.

What if I have a graph of a wavelike structure that is oscillating which I can use to measure for example: T (period), t (time), Δx (displacement), v (velocity), a (acceleration) and other variables is this possible? Gravity is not a factor in this example.

I realize that graphs are different cases. The second graph is more similar to the graph I might observe. I have been using them to conceptualize this issue and try to figure out how to rearrange different equations of Force (ma, -kx) without success.

I have been thinking that the answer could be approximated by solving for M using an equation applied to pendulums

M=4π²I/gDT²

and substituting the acceleration for gravity (which is not present in this case). Even though, this is different than a pendulum, perhaps there is a vector component of acceleration that is acting on each of the turning points of the waves that that acts in a similar fashion to gravity in a pendulum. Once I find this value I could then solve for the k constant.

Alternatively, maybe I could solve for k by using Uel(x) = 1/2kx² where the points of the graph are used to plot Uel(x) and then using this value and displacement solving for k by using k= d²Uel/dx².

Is there some better solution to solve for M and K or getting the approximate answer?

Last edited:
As the equation for y in the first picture tells you, the equations of motion depend on the ratio k/m. Analysing the motion can give you this ratio, but can't give you the actual values of k and m separately.

## 1. Can I determine the mass of an object from a graph of wave, time, and acceleration?

Yes, you can determine the mass of an object by using the formula m = F/a, where m is the mass, F is the force, and a is the acceleration. By analyzing the graph of wave, time, and acceleration, you can find the value of acceleration and use it in the formula to calculate the mass of the object.

## 2. How can I determine the spring constant (k) from a graph of wave, time, and vectors?

To determine the spring constant (k), you can use the formula k = F/x, where k is the spring constant, F is the force, and x is the displacement. By analyzing the graph of wave, time, and vectors, you can find the value of force and displacement and use them in the formula to calculate the spring constant.

## 3. Is it possible to determine both mass and spring constant from a graph of wave, time, acceleration, and vectors?

Yes, it is possible to determine both the mass and spring constant from a graph of wave, time, acceleration, and vectors. By analyzing the graph and using the formulas mentioned in the previous questions, you can calculate both the mass and spring constant of the object.

## 4. Can I determine the amplitude of the wave from a graph of wave, time, acceleration, and vectors?

Yes, you can determine the amplitude of the wave from a graph of wave, time, acceleration, and vectors. The amplitude of the wave is the maximum displacement from the equilibrium position, which can be found by analyzing the graph and identifying the highest and lowest points of the wave.

## 5. What other information can I determine from a graph of wave, time, acceleration, and vectors?

From a graph of wave, time, acceleration, and vectors, you can also determine the frequency and period of the wave. The frequency is the number of complete cycles of the wave per second, and the period is the time it takes for one complete cycle. These values can be found by analyzing the graph and using the appropriate formulas.

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