Proof of Equation for Period of Spring: T = 2pi (root x)/(root a)

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In summary, the conversation discusses a proof for the period of a spring using equations for centripetal acceleration and simple harmonic motion. While the proof is correct, it may not be the best approach for obtaining good marks as it includes other systems besides the spring itself. However, it effectively relates circular motion and oscillating motion.
  • #1
decamij
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I just want to know if the following proof is okay. I'm in grade 12, and i this will probably be on my midterm.

Prove the following equation (for the period of a spring):

T = 2pi x (root)x/(root)a

If: ac=v^2/r, and v = 2pirf, then:

ac = 4pi^2rf^2, and:

ac = (4pi^2r)/T^2. Therefore,

T = root(4pi^2r)/a

Therefore,

T = 2pi (root x)/(root a)
 
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  • #2
You equated it in a good manner but I don't thik it is good. You have taken centripetal acceleration in account but in an oscilating spring it is not possible.
To find it correctly, use t = 2 (pi)/f
find f for spring motion.
 
  • #3
But something in uniform circular motion and an ideal spring are both examples of simple harmonic motion
 
  • #4
yes, that's right, oscilating motion is also called as the projection of the circular motion. But when you are giving a proof for oscilating spring than you must take only spring i system in account, you can reffer to other relative systems, but relate them with the required system.
this proof is good to relate the circular motion and the oscillating motion but not good to obtain nice marks.
 

1. What is the equation for the period of a spring?

The equation for the period of a spring is T = 2pi (root x)/(root a), where T is the period (in seconds), x is the mass attached to the spring (in kg), and a is the spring constant (in N/m).

2. How is the period of a spring affected by the mass attached to it?

The period of a spring is directly proportional to the square root of the mass attached to it. This means that as the mass increases, the period also increases. However, the effect of mass on the period is not linear, as doubling the mass will not double the period. It will only increase it by a factor of square root of 2.

3. How does the spring constant affect the period of a spring?

The spring constant, represented by the variable a in the equation, is inversely proportional to the period of a spring. This means that as the spring constant increases, the period decreases. However, like the effect of mass, this relationship is not linear. Doubling the spring constant will only decrease the period by a factor of square root of 2.

4. Why is there a 2pi in the equation for the period of a spring?

The 2pi in the equation is a constant factor that represents the full cycle of a sine wave. The period of a spring is determined by the oscillations of the mass attached to it, which follow a sine wave pattern. Therefore, the 2pi is included in the equation to account for the full cycle of the wave.

5. Can this equation be used for all types of springs?

Yes, this equation can be used for any type of spring, as long as the mass is attached to the end of the spring and there is no external force acting on the system. This equation is a fundamental law of physics and applies to all springs, regardless of their shape or size.

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