Horizontal spring-block system

[Blogical]

Can anybody derive and give the formula for the time period of a spring-block system placed horizontally having a spring with a definite mass 'm"?
Considering it will still execute periodic motion or else what will be the physical nature of such a system?

 

[AlephZero]

If you want an approximate solution for the lowest frequency of the system, assume the spring stretches linearly along its length and find its kinetic energy in terms of the velocity of the block. IIRC, ths is the same as adding m/3 to the mass of the block.

If you want an exact solution, set up the equations of motion for the spring (which is equivalent to the wave equation) and solve it with the boundary conditions (fixed at one end and the block attached to the other).

 

[Blogical]

If you want an approximate solution for the lowest frequency of the system, assume the spring stretches linearly along its length and find its kinetic energy in terms of the velocity of the block. IIRC, ths is the same as adding m/3 to the mass of the block.

If you want an exact solution, set up the equations of motion for the spring (which is equivalent to the wave equation) and solve it with the boundary conditions (fixed at one end and the block attached to the other).

Is the approximate solution equivalent to that of the vertical spring-block system where it is by adding m/3?
How can that be possible?
How to set the equation when the spring has mass, won't the physics be different??