Period of oscillation for a mass on a spring

[physics20]

Why does the period of oscillation for a mass on a spring depend on its mass? (while in other situations, like a simple pendulum, the mass seems to be unimportant)

 

[hotvette]

Reason is the amount of spring deflection is proportional to the attached mass. If mass is very small, the spring doesn't deflect very much and takes a much short time to complete a cycle than if the mass was large.

 

[granpa]

because the restoring force for a pendulum is due to gravity
for a larger mass the restoring force is automatically larger.
that is not the case for a mass-spring system

 

[nasu]

Reason is the amount of spring deflection is proportional to the attached mass. If mass is very small, the spring doesn't deflect very much and takes a much short time to complete a cycle than if the mass was large.

This is a little confusing and mostly not true.
The period does not depend on the spring deflection (amplitude) and the amplitude does not depend on the mass attached but on the initial conditions.
If you have in mind a vertical spring (it does not have to be vertical) with a mass attached, then the mass determines the equilibrium deflection, but this is not in general related to the amplitude or the period of the oscillations.

 

[PJC01]

The period of oscillation for a mass on a spring is dependent on its mass because of the relationship between mass and inertia. Inertia is the tendency of an object to resist changes in its state of motion. In the case of a mass on a spring, the mass provides the inertia that is necessary for the oscillation to occur. The greater the mass, the greater the inertia, and therefore, the longer the period of oscillation.

On the other hand, in a simple pendulum, the mass does not affect the period of oscillation because the inertia is provided by the length of the pendulum and the gravitational force acting on the mass. In this case, the mass only affects the amplitude of the oscillation, not the period.

It is important to note that the period of oscillation for a mass on a spring can also be affected by other factors such as the stiffness of the spring and the amplitude of the oscillation. However, the mass remains a crucial factor in determining the period of oscillation in this system.

In conclusion, the period of oscillation for a mass on a spring depends on its mass due to the role of inertia in the oscillation process. This is in contrast to other systems, such as a simple pendulum, where the mass plays a less significant role in determining the period of oscillation.