Finding spring constant from a graph

[John Sena]

Assume a spring with a mass attached is oscillating.
Can i find spring constant from force/time and position/time graph using mgh=1/2kx^2?
The force in force/time graph is collected from force meter attached at the top of the spring.
The positin in position/time graph is the distance of the mass from the ground.

 

[Quantum Defect]

Assume a spring with a mass attached is oscillating.
Can i find spring constant from force/time and position/time graph using mgh=1/2kx^2?
The force in force/time graph is collected from force meter attached at the top of the spring.
The positin in position/time graph is the distance of the mass from the ground.

If you write a function for x(t) what do you get? x(t) = x(t=0) + ... Does this expression have k anywhere? How does this relate to an important time interval?

 

[Chestermiller]

Draw a free body diagram for the mass, and write a force balance for the mass. What do you get?

Chet

 

[ZapperZ]

Assume a spring with a mass attached is oscillating.
Can i find spring constant from force/time and position/time graph using mgh=1/2kx^2?
The force in force/time graph is collected from force meter attached at the top of the spring.
The positin in position/time graph is the distance of the mass from the ground.

There is something not quite clear here and it requires a bit more explanation.

First of all, is this something that is part of a measurement or experiment? Are you simply given a spring with a mass, and it is ALREADY oscillating? How accurate do you need this to be?

You see, if this is simply an experiment or an observation, you can easily calculate the spring constant by simply measuring the frequency of oscillation. Measure how many times the mass makes a complete oscillation in one second, and you have the frequency of oscillation. Then simply use the fact that for a SHO system,

f = (1/2pi)*(sqr(k/m)

Knowing the mass, you immediately get the value of k.

Asking if you can find the spring constant from the force-time or position-time graph is vague. Were you GIVEN these or were you asked to measure these?

Zz.

 

[PJC01]

Yes, it is possible to find the spring constant from a graph of force vs. time and position vs. time. However, it is important to note that the equation mgh=1/2kx^2 is not applicable in this scenario. This equation is used for calculating potential energy, not the spring constant.

To find the spring constant, you can use the equation F = -kx, where F is the force applied by the spring, k is the spring constant, and x is the displacement from the equilibrium position. By analyzing the force vs. time and position vs. time graphs, you can determine the maximum force and maximum displacement of the spring. Then, you can use the equation F = -kx to calculate the spring constant.

It is also important to make sure that the spring is behaving in a linear manner, meaning that the force applied by the spring is directly proportional to the displacement. If the graph is not linear, the spring constant cannot be accurately determined.

In conclusion, while it is possible to find the spring constant from a graph, it is important to use the correct equation and ensure that the spring is behaving in a linear manner.