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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Cameron Wallace · Accepted Answer

Start with the equation for the period  T  =  2  π            m      k      , whereT-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

aurelegena · Accepted Answer

Let&#039;s say we started from   ω  =            k      m      . It&#039;s a bit different but a similar approach.If we examine the equation  y  =  A  sin  ⁡  (  n  θ  +  ϕ  )  +  kIf 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

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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