A spring with spring constant k is suspended vertically from...

A spring with spring constant $k$ is suspended vertically from a support and a mass $m$ is attached. The mass is held at the point where the spring is not stretched. Then the mass is released and begins to oscillate. The lowest point in the oscillation is $20 \mathrm{cm}$ below the point where the mass was released. What is the oscillation frequency?

Key Concepts

Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from its rest position, with the spring constant k as the proportionality factor. This principle is fundamental in understanding the restoring forces in systems where elastic deformation occurs, such as in a mass-spring system undergoing oscillations.

Simple Harmonic Motion (SHM)

Simple harmonic motion describes a type of periodic oscillation where the restoring force is proportional to the displacement and acts in the opposite direction. In a mass-spring system, the motion is sinusoidal and is characterized by parameters such as amplitude, angular frequency, and period, which are directly related to the mass and the spring constant.

Equilibrium Position in a Vertical Spring System

In a vertically suspended spring with a mass attached, the equilibrium position is the point where the spring force balances the gravitational force acting on the mass. This leads to a static stretch given by mg/k. When the mass is released from a point other than the equilibrium, it oscillates about this equilibrium position.

Oscillation Frequency

The oscillation frequency of a mass-spring system in simple harmonic motion is determined by the properties of the system, specifically the mass and the spring constant. The frequency is given by f = (1/(2?))?(k/m), which indicates how many complete oscillations occur each second. This relation is a central concept in the study of oscillatory systems.

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