Simple Harmonic Motion: Period Calculation and Newton's Second Law Explanation

AI Thread Summary
The discussion centers on calculating the period of simple harmonic motion for a mass attached to a spring. The mass falls 49 cm and oscillates around its equilibrium position, prompting the need to determine the period using Newton's second law. The correct formula for the period is T=2π√(m/k), where k is the spring constant. The user initially miscalculated the angular frequency, leading to confusion about the expected result of π/√10. The explanation clarifies that k can be found by balancing gravitational and elastic forces at the midpoint of the motion.
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Homework Statement



A spring is freely hanged on a ceiling. You attach a mass to the end of the spring and let the mass go. It falls down a distance of 49 cm and comes back to where it started. It contineous to oscillate in a simple harmonic motion going up and down - a total distance of 49 cm from top to bottom. What is the period of the simple harmonic oscillation?

Homework Equations



Newtons Second Law --->> Fr = Fg

The Attempt at a Solution



To find the period of the simple harmonic motion, my first objective was to find the angular frequency using the equation (k/m) = (g/Xm) which comes from Newtons second law, however the answer I am suppose to get is ∏/\sqrt{}10 but i got ∏\sqrt{}10 ---> please explain how it works
 
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Show your work, please. How did you get that result? What is Xm?

ehild
 
Given that the period of the armonic motion of the spring is given by
$$T=2\pi\sqrt{\frac{m}{k}}$$
the only thing you need to find is indeed ##k##. You did correctly finding the equilibrium situation; indeed in the middle of the motion (means @##x_{1/2}=24.5## cm) you have the gravitational force balancing the elastic one (the mass goes on because at that point it has a speed, but you do not care about this). Therefore you can find ##k## imposing
$$kx_{1/2}=mg$$
and the trick is done. Plugging numbers I indeed find ##\pi/\sqrt{10}##.
 
Thanks tia89, ill provide the whole work out in the next question - I am new to the forum and I am not very good at inserting equations etc. Please understand ...
 

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