Simple harmonic frequency clarification

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SUMMARY

The frequency of oscillation for a massless spring with a spring constant of 23.5 N/m and a mass of 0.30 kg is calculated using the formula f = (1/2π)√(k/m). The correct calculation yields a frequency of approximately 8.85 Hz, not 13.90 Hz as initially suggested. The confusion arose from a miscalculation involving the division by 2π, which is approximately 6.28. Therefore, the correct frequency is 8.85/6.28, resulting in a frequency of approximately 1.41 Hz.

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  • Understanding of simple harmonic motion
  • Familiarity with spring constants and mass
  • Basic knowledge of trigonometric functions and π
  • Ability to perform square root and division calculations
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  • Review the principles of simple harmonic motion and its equations
  • Learn about the relationship between spring constant and oscillation frequency
  • Practice calculations involving mass-spring systems
  • Explore the effects of varying mass and spring constants on frequency
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Students in physics, engineers working with mechanical systems, and anyone interested in understanding oscillatory motion and its calculations.

Rasine
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A massless spring with spring constant 23.5 N/m hangs vertically. A body of mass 0.30 kg is attached to its free end and then released. Assume that the spring was unstretched before the body was released.

What is the frequency of oscillation of the resulting motion, assumed to be simple harmonic?

ok so f=(1/2pi)[sqroot(k/m)] because w=sqroot(k/m) and f=w/2pi

so i have (1/2pi)[sqroot(23.5/.30)] which is 13.90...right?

and the units would be Hz right because w is in rad/s and that divided by rad would give cycles/s


i think i am doing something wrong. please point it out to me.
 
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Rasine said:
so i have (1/2pi)[sqroot(23.5/.30)] which is 13.90...right?

Your thinking and your equation are OK. Maybe your calculator is broken :smile:

Hint: my calculator says sqrt(23.5/0.3) = 8.85
 
thats what i get too but the formula says that 8.85 should be divided by 2pi which is 13.90

is that calculation right? should i do that?
 
On my calculator 8.85 x PI / 2 = 13.90. I guess you are pushing the wrong buttons.

2pi is about 6.28. There is no way that 8.85/6.28 could be 13.90 !
 

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