Solve Spring Frequency Homework: .88kg to .4kg

In summary, the conversation discusses the calculation of the new frequency of vibration when the mass is decreased from 0.88 kg to 0.4 kg in a system with a light-weight spring. The equation used to solve this problem is P = 2π√(m/k). However, there are two different methods used to solve the equation, resulting in slightly different answers. The discrepancy is explained by the use of the incorrect equation, as the correct equation is 2πf = √(k/m).
  • #1
jdeakons
3
0

Homework Statement


A mass of .88 kg when fastened to the lower end of a light-weight spring and set vibrating up and down is found to have a frequency of 1.8 Hz. Calculate the new frequency of vibration when the mass is decreased to .4 kg.

Homework Equations


P = 2 [tex]\pi[/tex] [tex]\sqrt{m/k}[/tex]

The Attempt at a Solution


Using K = (m 4 [tex]\pi[/tex]^2 ) / P^2, my answer for K comes out to 112.56.

But, using [tex]\sqrt{k}[/tex] = ([tex]\sqrt{m}[/tex] 2 [tex]\pi[/tex] )/ P, I get 3.2572. But how can that be? The equations are the same, aren't they? Where am I making the mistake?

Thanks.
 
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  • #2
[tex]2\pi f=\sqrt{\frac{k}{m}}[/tex]
 
  • #3


There is no mistake in your calculations. The two equations you used are actually different forms of the same equation. The first equation, P = 2 \pi \sqrt{m/k}, is the equation for the period of a simple harmonic oscillator, where m is the mass and k is the spring constant. The second equation, \sqrt{k} = (\sqrt{m} 2 \pi )/ P, is the equation for the angular frequency of a simple harmonic oscillator, where P is the period. In your case, you have calculated the spring constant k using the first equation and then used it in the second equation to calculate the new angular frequency. This is why you are getting different numbers.

To calculate the new frequency, you can use the equation P = 2 \pi \sqrt{m/k} again, but this time plug in the new mass of 0.4 kg. You should get a new frequency of 2.4 Hz. Keep in mind that the frequency is directly proportional to the square root of the mass, so as the mass decreases, the frequency will increase.
 

1. What is the formula for calculating spring frequency?

The formula for calculating spring frequency is f = 1 / (2π√(m/k)), where f is the frequency, m is the mass of the object attached to the spring, and k is the spring constant.

2. How do you convert mass from .88kg to .4kg?

To convert mass from .88kg to .4kg, you can simply multiply .88 by .4, which equals .352kg. This is the new mass value that can be used in the spring frequency formula.

3. Can the spring frequency change if the mass of the object changes?

Yes, the spring frequency will change if the mass of the object attached to the spring changes. This is because the mass value is included in the spring frequency formula, so any changes in mass will affect the frequency.

4. What is the significance of spring frequency in science?

Spring frequency is an important concept in science because it helps us understand the behavior of springs and how they respond to different forces. It is also used in various fields such as mechanics, engineering, and physics.

5. How does changing the spring constant affect the spring frequency?

The spring frequency is directly proportional to the square root of the spring constant. This means that if the spring constant increases, the frequency also increases, and vice versa. Therefore, changing the spring constant will have a direct effect on the spring frequency.

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