A spring is hung from the ceiling. When a block is attached...

A spring is hung from the ceiling. When a block is attached to its end, it stretches $2.0 \mathrm{cm}$ before reaching its new equilibrium length. The block is then pulled down slightly and released. What is the frequency of oscillation?

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Key Concepts

Equilibrium Condition

In a spring-mass system, the equilibrium position is reached when the downward gravitational force on the mass is exactly balanced by the upward spring force. This condition allows for the determination of the spring constant by setting mg = kx, where m is the mass, g is the gravitational acceleration, and x is the displacement from the spring's natural length.

Simple Harmonic Motion

Simple harmonic motion (SHM) describes the oscillatory movement of a system where the restoring force is proportional to the displacement from equilibrium. For a mass-spring system, the angular frequency is given by ? = sqrt(k/m), and the regular frequency can be calculated using f = ?/(2?). This concept underpins the analysis of oscillatory behavior in such systems.

Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position. This relationship is usually expressed as F = -kx, where k is the spring constant and x is the displacement. It is fundamental to understanding the restoring force that acts on a mass attached to a spring.

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