Calculating the Constant k in a Spring Pendulum System

[brandon26]

I think this question is complicated, and I don't even know how to start it off, please help?

A mass of 2 kg is hung from the lower end of a spiral spring and extends it by 0.4m. When the mass is displaced a further short distance x and released, it oscillates with acceleration a towards the rest position. If a = -kx and if the tension in the spring is always directly proportinal to its extension, what is the value of the constant k?

Please help, this urgent, I am revising for a physics exam that is coming up next week.

 

[El Hombre Invisible]

First off, the restoring force F = -kx, not a = -kx.
Secondly, I assume x is horizontal? So this is a pendulum motion?
Thirdly, I assume that the original length of the spring is, if unknown, negligible.
Fourthly, the horizontal displacement is small enough to neglect the vertical motion of the pendulum.

The restoring force is then:

F = -kx = -mgx/l.

This gives you k = mg/l, all of which are given. This depends on how I've interpreted your question, so let me know if any of the above four assumptions conflict with any extra info you've been given.

Fifth assumption - S207? In the same boat, if so.

 

[quicknote]

I understand that this question may seem complicated and overwhelming at first. However, by breaking down the problem into smaller steps and using the relevant equations and principles, we can easily determine the value of the constant k in this spring pendulum system.

Firstly, let's review the given information. We have a mass of 2 kg hanging from the lower end of a spiral spring, which extends the spring by 0.4m. When the mass is displaced a further distance x and released, it oscillates with acceleration a towards the rest position. We are also given the relationship between acceleration and displacement, which is a = -kx. This means that the acceleration is directly proportional to the displacement, with the constant of proportionality being -k.

Next, we need to consider the tension in the spring. The tension in the spring is always directly proportional to its extension. This means that as the spring extends, the tension in the spring increases proportionally. This is described by the equation F = -kx, where F is the tension in the spring and x is the extension.

Now, we can use Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, the net force is the tension in the spring (F) and the mass is 2 kg. Therefore, we can rewrite the equation as -kx = 2a.

We also know that the acceleration (a) is directly proportional to the displacement (x), so we can substitute -kx for a in the equation. This gives us -kx = 2(-kx). By rearranging this equation, we can determine the value of the constant k.

-kx = -2kx
x = 2x
1=2

This is a contradiction, as 1 cannot be equal to 2. Therefore, there must be an error in our calculations or assumptions. Upon further inspection, we can see that the given information is not sufficient to determine the value of the constant k. We would need to know the value of either the acceleration or the displacement in order to solve for k.

In conclusion, as a scientist, it is important to carefully analyze and consider all given information before attempting to solve a problem. In this case, it is not possible to determine the value of the constant k without additional information. I would recommend revisiting