A horizontal spring is attached to a 5 kg block. When the...

A horizontal spring is attached to a 5 kg block. When the block is pulled 5 cm to the right, the restoring force has a magnitude of 6 N. What is the frequency of the spring?
(A) 0.32 Hz
(B) 0.56 Hz
(C) 0.78 Hz
(D) 0.98 Hz

Key Concepts

Hooke's Law

This fundamental principle of mechanics states that the restoring force exerted by a spring is directly proportional to the displacement from its equilibrium position. It is usually expressed as F = -kx, where F is the force, k is the spring constant, and x is the displacement. This concept is key in understanding how springs behave under deformation.

Spring Constant

The spring constant, denoted by k, quantifies a spring's stiffness and is defined as the force required to produce a unit displacement. It is calculated by dividing the applied force by the displacement, which is essential for determining the characteristics of systems that exhibit elastic behavior.

Simple Harmonic Motion

Simple harmonic motion (SHM) describes the oscillatory movement of systems where the restoring force is directly proportional to the negative displacement, such as in a mass-spring system. SHM is characterized by sinusoidal oscillations and consistent frequency, making it fundamental for analyzing periodic phenomena in physics.

Frequency Calculation in Mass-Spring Systems

For a mass attached to a spring undergoing simple harmonic motion, the frequency of oscillation can be calculated using the formula f = (1/(2?))?(k/m), where k is the spring constant and m is the mass. This formula is important for predicting the oscillatory behavior of the system from its physical parameters.

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