Find Frequency of Spring with Mass & Length Connected to Rigid Wall

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To find the frequency of a spring with mass m and length L connected to a rigid wall and a mass M, the effective mass of the spring is considered to be one-third of its total mass. The kinetic energy (KE) of an infinitesimal element of the spring, dm, is expressed as 1/2 dm * v^2, where the velocity v varies along the length of the spring. By defining the velocity of each element as proportional to its distance from the fixed end, and integrating the KE over the length of the spring, one can determine the total kinetic energy and effective mass. This approach leads to the calculation of the system's frequency of oscillation. Understanding these principles allows for accurate frequency determination in this mechanical system.
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Suppose a spring with mass m and length L is connected to a rigid wall and a mass of M. Assuming no damping how do we find the frequency?

for the spring Density = m/L = D; dm = D dx
I don't know where to go from there.
 
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The effective mass of a spring undergoing oscillatory motion is considered
to be 1/3 the mass of the spring. For any portion of the spring the
KE of dm is 1/2 dm * v^2. For a spring fixed at one end the velocity of an
element dm will be proportional to the distance from the fixed end - so
v = V*(y/Y) where Y is the length of the spring and V is the velocity of the moving end. Also, you can write dm = M * (dy/Y). Using these values
integrate 1/2 v^2 dm over the length of the spring to get the KE of the
oscillating spring and determine the effective mass of the spring.
 
Thanks, I understand now.
 

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