Physics

posted by Kim

I'm haivng troulbe proving the deriviation of this formula on my own...

could you please help me derive the proof of the formula or maybe show me one thansk...

I need to prove this formula

period of a mass spring system in simple harmonic motion

T = 2 pi square root of (m/k)
period = 2 pi X square root of (mass divided by spring constant)

thanks

  1. Damon

    F = m a
    F = -k x for spring of constant k in N/m
    so
    m a = - k x
    now assume motion of form x = A sin (2 pi f t)
    then
    dx/dt = velocity = A (2 pi f) cos 2 pi f t)
    then
    d velocity/dt = a = -A (2 pi f)^2 sin (2 pi f t)
    or in other words
    a = - x (2 pi f)^2
    so
    - k x = m [ - x (2 pi f)^2 ]
    or
    (2 pi f)^2 = k/m
    so
    2 pi f = sqrt (k/m)
    but T = 1/f
    so
    T = 2 pi sqrt (m/k)

Respond to this Question

First Name

Your Answer

Similar Questions

  1. AP Physics

    Hello I was trying to find the proof of the formula x = x0 + v0t +.5at^2 were the zeros are subscripts My text book dosen't explain it that well. ok well it involves the formula for average velocity aver velocity = 2^-1(v0 + v) were …
  2. AP Physics

    I'm trying to derive the formula v^2 = v0^2 + 2a(x-x0) were zeros are subscripts my book tells me to derive it this way use the definition of average velocity to derive a formula for x use the formula for average velocity when constant …
  3. Physics PLEASE

    I'm trying to derive the formula v^2 = v0^2 + 2a(x-x0) were zeros are subscripts my book tells me to derive it this way use the definition of average velocity to derive a formula for x use the formula for average velocity when constant …
  4. PreCalculus REINY HELP PLEASE

    well yay thanks for the answer but i really need the formula lol I tried to derive it on my own but it was a little bit rough lol i need the formula it wasn't in my book and I don't know what the name of the formula would be so i can't …
  5. Chemistry

    the formula H2O2 is an example of 1.molecular formula 2. an empirical formula 3.an ionic formula 4.an organic formula
  6. Chemistry

    Derive a formula for the molar mass of the solute in terms of the freezing point depression, deltaT, the freezing-point constant, Kf, and the masses of solvent, msolvent, and solute, msolute, used in an experiment like this one. SHow …
  7. chemistry

    Derive the empirical formula of a hydrocarbon that on analysis gave the following percentage by mass composition: C = 85.63 % and H = 14.37 %. If the molecular mass of this compound is 56 g, derive the molecular formula.
  8. Geometry

    What formula should be used to derive the equation of a parabola given its focus and directrix?
  9. Calculus

    I apologize if this question is too much to ask on this site, but I am really confused. Any help would be greatly appreciated. The famous formula shown below is called Euler’s formula, after the Swiss mathematician Leonhard Euler …
  10. pre calculus

    ea + bi = ea(cos b + i sin b) This formula gives rise to the equation eπi + 1 = 0. . Show how Euler’s formula can be used to derive this equation.

More Similar Questions