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How to calculate velocity in a spring mass model?

  1. Aug 9, 2012 #1
    1. The problem statement, all variables and given/known data

    At time t = 0, the mass is released 8 mm below the static equilibrium position. The mass is
    m = 4kg and each spring stiffness is k = 40 kN/m.
    Determine:
    (i) The equivalent spring stiffness.
    (ii) The natural frequency of the system in Hertz.
    (iii) The displacement equation of the spring-mass model.
    (iv) The velocity of the mass at time t = 0.05s.
    (v) The acceleration of the mass at time t = 0.05s.

    2. Relevant equations

    x=A sin⁡〖ω_n 〗 t+B cos⁡〖ω_n 〗 t


    3. The attempt at a solution I have managed to calculate it. Basically B is equal to displacement at t=0 according to lectures about undamped free vibration and A is equal to velocity x/natural circular frequency. In order to find velocity, I calculated natural circular frequency using the W=square root of (stiffness(k)/mass(m)) and after it I differentiated the formula for x given above in the relevant equations. Pretty much I just have to replace B for displacement and then multiplied by natural frequency in the derived velocity formula. A would be ignored and the value for B times W_n would be used as the value for velocity I believe. The derivation of the above formula should be something like this:

    x=ω_n A cos⁡〖ω_n 〗t - ω_n B sin⁡〖ω_n 〗t

    This is about undamped free vibration for Dynamics. If someone knows about it, would be nice if they could give me a shout and let me know if Im wrong and add some input into it here in the thread
     
    Last edited: Aug 9, 2012
  2. jcsd
  3. Aug 9, 2012 #2
    Velocity found. For acceleration I need to differentiate the formula for velocity and use the same method I think.
     
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