A 200 g air-track glider is attached to a spring. The glider...

A $200 \mathrm{g}$ air-track glider is attached to a spring. The glider is pushed in $10 \mathrm{cm}$ and released. A student with a stopwatch finds that 10 oscillations take $12.0 \mathrm{s}$. What is the spring constant?

Key Concepts

Hooke's Law

Hooke's Law is a foundational principle that states the force exerted by a spring is proportional to the displacement from its equilibrium position, mathematically represented as F = -kx. This law is essential for understanding the motion of systems that exhibit simple harmonic motion and for deriving the period of oscillation in mass-spring systems.

Oscillation Period

The oscillation period is the time it takes for an oscillating system to complete one full cycle of its motion. In the context of a mass-spring system undergoing SHM, this period is crucial for analyzing the system’s motion and is given by the formula T = 2??(m/k), linking the mass and the spring constant.

Spring Constant

The spring constant is a measure of a spring's stiffness, defined as the ratio of the force exerted by the spring to the displacement it causes (k = F/x). It is a key parameter in determining the dynamics of a mass-spring system, particularly in relating the system's mass and oscillation period through the equation T = 2??(m/k).

Simple Harmonic Motion

Simple Harmonic Motion (SHM) refers to the oscillatory movement in which the restoring force is directly proportional to the displacement and acts in the opposite direction. This type of motion is characterized by its sinusoidal nature, with periodic oscillations that can be described using mathematical functions and constants.

Mass-Spring System

A mass-spring system is a fundamental model in physics where a mass is attached to a spring. When displaced from its equilibrium position, the restoring force provided by the spring causes the mass to oscillate. This system is commonly used to study principles of dynamics and energy conservation in simple harmonic motion.

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