Solving a System of ODEs in Mass-Spring Dynamics

AI Thread Summary
The discussion focuses on formulating a system of ordinary differential equations (ODEs) for a mass-spring system involving two identical masses connected by springs. The proposed equations for the displacements x1 and x2 are mx1'' = -k[x1-f(t)] + k[x2-x1-f(t)] and mx2'' = -k[x2-x1-f(t)]. Participants emphasize the importance of correctly accounting for the forces exerted by the springs, noting the influence of the spring constants and the external displacement f(t). There is a call for clarification on the spring constants and their effects on the forces involved. The conversation highlights the need for careful analysis in deriving the equations of motion for such dynamic systems.
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Homework Statement



Two identical masses m1 = m2 = m are connected by a massless spring with
spring constant k. Mass m1 is attached to a support by another massless spring with
spring constant 2k. The masses and springs lie along the horizontal x-axis on a smooth
surface. The masses and the support are allowed to move along the x-axis only. The
displacement of the support in the x-direction at time t is given by f (t) and is externally
controlled. Write down a system of differential equations describing the evolution of the
displacements x1 and x2 of the masses from their equilibrium positions.


Homework Equations





The Attempt at a Solution



Is it: mx1'' = -k[x1-f(t)] + k[x2-x1-f(t)]

mx2" = -k[x2-x1-f(t)]

?

Thanks!
 
Physics news on Phys.org
Check your equations. The force exerted by a spring depends on the change of its length. Does an other spring effect this force?
Read the problem, are the spring constants equal?

ehild
 
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