How do you find what the mass on the spring is if you know the period and force constant of the harmonic oscillator?

Damon Vazquez 2022-09-01 Answered
How do you find what the mass on the spring is if you know the period and force constant of the harmonic oscillator?
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Answers (2)

Cameron Wallace
Answered 2022-09-02 Author has 8 answers
Start with the equation for the period
T = 2 π m k , where
T-the period of oscillation;
m- the mass of the oscillating object;
k- a constant of proportionality for a mass on a spring;
You need to solve this equation for m, so start by squaring both sides of the equation
T 2 = ( 2 π m k ) 2
T 2 = ( 2 π ) 2 ( m k ) 2
T 2 = 4 π 2 m k
Now all you have to do is isolate m on one side of the equation
T 2 k = 4 π 2 m
m = T 2 k 4 π 2 = k T 2 4 π 2
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aurelegena
Answered 2022-09-03 Author has 2 answers
Let's say we started from ω = k m . It's a bit different but a similar approach.
If we examine the equation
y = A sin ( n θ + ϕ ) + k
If n was doubled, the frequency would be doubled, but the period would be halved. So, we know that ω 1 T
If ω is 2 π r a d / s, the period T is 1 s, so to create the equality between the two variables, we match up the units by multiplying 1 T by 2 π r a d to get ω = 2 π T
ω = 2 π T = k m
Square both sides:
4 π 2 T 2 = k m
Reciprocate both sides and then multiply by k:
m = k T 2 4 π 2
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