Is the approximate solution equivalent to that of the vertical spring-block system where it is by adding m/3?AlephZero said: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).
A horizontal spring-block system is a mechanical system consisting of a block attached to a horizontal spring. The spring provides a restoring force that acts on the block as it moves back and forth.
The components of a horizontal spring-block system include a block, a horizontal spring, and a surface on which the block can slide. In some cases, additional components such as a mass and a damping device may also be present.
The equation of motion for a horizontal spring-block system is given by F = ma = -kx - bv, where F is the net force on the block, m is the mass of the block, k is the spring constant, x is the displacement of the block from its equilibrium position, b is the damping coefficient, and v is the velocity of the block.
The behavior of a horizontal spring-block system is affected by several factors, including the mass of the block, the spring constant, the damping coefficient, and the amplitude and frequency of the oscillations. The surface on which the block slides may also have an impact on the system's behavior.
Horizontal spring-block systems have a variety of applications in engineering and physics, such as in shock absorbers, vibration isolators, and seismic sensors. They are also commonly used in physics demonstrations and experiments to study simple harmonic motion.