Mass spring system Definition and 55 Threads

In a real spring–mass system, the spring has a non-negligible mass



m


{\displaystyle m}
. Since not all of the spring's length moves at the same velocity



v


{\displaystyle v}
as the suspended mass



M


{\displaystyle M}
, its kinetic energy is not equal to






1
2



m

v

2




{\displaystyle {\tfrac {1}{2}}mv^{2}}
. As such,



m


{\displaystyle m}
cannot be simply added to



M


{\displaystyle M}
to determine the frequency of oscillation, and the effective mass of the spring is defined as the mass that needs to be added to



M


{\displaystyle M}
to correctly predict the behavior of the system.

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  1. N

    Solving Mass Spring System Collision ODEs

    Good day all, I've got a rather puzzeling question on hand that is part of my Dynamic project. I need to model the collision of two vehicles. Each vehicle is traveling head on to the other, and each one has a spring attached to its front. We can assume that the final velovity after collision...
  2. F

    What is the natural frequency of an unequal mass spring system?

    Hey guys Im revising for my end of year exams and this was a question i got wrong in a test we had this year and unforunately there arent worked answers. I sort of get close but not quite there. The answer is A, which i get, sorta F = ma = 2kx As per Newtons third law (the hint) saying that...
  3. F

    Mass Spring System: Solving for Motion Over Time

    In a vertical mass spring system, spring with spring constant 250 N/m vibrates with an amplitude of 12cm when 0.38kg hangs from it. What is the equation describing this motion as a function of time? ( assume the mass passes through the equilibrium point, towards the positive x(upward), at t =...
  4. R

    Can You Prove Simple Harmonic Motion for a Mass Spring System?

    I've been trying this question for quite some time and have given up. Prove that a mass,M , suspended from a fixed point by a helical spring, which obeys hooke's law, undergoes simple harmonic motion when it is displaced vertically from its equilibrium position. Say I displace the mass...
  5. L

    Find Spring Constant (k) in Mass Spring System

    I've a question.. and don't know what to do An object of mas (m) is traveling on a horizontal surface. There is a coefficient of kinetic firction (mu) between the object and the surface. The object has speed (v) when it reaches (x=0) and encounters a spring. The object compress the spring...
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