Explain the motion of mass attached to Spring placed on a horizontal surface
When a mass is attached to a spring and placed on a horizontal surface, the motion of the mass can be described by simple harmonic motion (SHM). In SHM, the mass oscillates back and forth around its equilibrium position.
The equilibrium position is the position where the spring is not stretched or compressed and has no net force acting on it. When the mass is displaced from this equilibrium position, a restoring force is exerted by the spring that tries to bring the mass back to its equilibrium position. The restoring force is proportional to the displacement from equilibrium and is directed opposite to the displacement.
According to Hooke's Law, the restoring force (F) exerted by the spring is given by F = -kx, where k is the spring constant and x is the displacement from equilibrium.
When the mass is initially displaced and released, it experiences the restoring force and starts to move towards the equilibrium position. As it approaches the equilibrium position, the restoring force decreases and eventually becomes zero when the mass reaches the equilibrium position. However, due to its inertia, the mass continues to move past the equilibrium position.
Now, the spring starts to exert a restoring force in the opposite direction, trying to bring the mass back towards the equilibrium position. As the mass moves away from equilibrium, the restoring force increases again.
This process continues, with the mass oscillating back and forth around the equilibrium position. The mass reaches maximum displacement on either side of the equilibrium position known as the amplitude of the motion. The period of oscillation, T, which is the time taken for one complete oscillation, depends on the mass (m) and the spring constant (k) and is given by T = 2π√(m/k).
The motion of the mass attached to a spring on a horizontal surface can be influenced by external factors such as friction. Friction can cause the amplitude of the motion to decrease gradually, resulting in damping of the oscillations. However, in the absence of significant friction, the motion is nearly ideal SHM.