Simple Harmonic Motion-Period of oscillations

AI Thread Summary
The discussion centers on calculating the period of oscillations for a mass-spring system, specifically a 10kg mass attached to a spring with a spring constant of 20 N/m. The user correctly applies the formula for angular frequency, ω = √(k/m), resulting in ω = 1.41. They then use the relationship ω = 2π/T to find the period T, calculating it as approximately 4 seconds. There is uncertainty regarding the accuracy of the algebra used to solve for T and whether the final answer should be rounded to one significant figure. Overall, the calculations appear correct, and the rounding to one significant figure is appropriate given the provided data.
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Homework Statement



What is the period of oscillations of a spring fixed to the ceiling at one end and set in motion by attaching a mass 10kg to the other end? The spring constant is 20 N/m.

Homework Equations



I used equations found in my lab book for Simple Harmonic Motion.

ω=√k/m

Then I used the equation ω=2pi/T to solve for T


The Attempt at a Solution



I used equations found in my lab book for Simple Harmonic Motion.
First I found
ω according to ω=√k/m
ω=√20/10
ω=√2
ω=1.41

Then I used the equation ω=2pi/T to solve for T
1.41 = 2pi/T
1.41(T)=2pi
T=2pi/1.41
T=4
I rounded T to only 1 significant figure, the same as the given mass and spring constant.

I have a final answer (4) but I am not sure I did this problem correctly, and I am unsure of my algebra where I solved for T. Also, would it be rounded to 1 significant figure?
Any insight would be great. Thanks!
 
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Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

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