An object in simple harmonic motion has amplitude 4.0 cm and...

An object in simple harmonic motion has amplitude 4.0 $\mathrm{cm}$ and frequency $4.0 \mathrm{Hz},$ and at $t=0 \mathrm{s}$ it passes through the equilibrium point moving to the right. Write the function $x(t)$ that describes the object's position.

Key Concepts

Phase Constant

The phase constant (or phase shift) is an angular parameter that accounts for the initial conditions of the motion, such as the object's starting position and direction of motion. It determines where in its cycle the oscillation begins.

Frequency

Frequency is the number of oscillations or cycles completed per unit time, typically measured in hertz (Hz). It defines how rapidly the oscillation occurs and is inversely related to the period of the motion.

Sinusoidal Function

A sinusoidal function, either in the form of sine or cosine, is used to model simple harmonic motion. These functions represent the displacement of the object over time and incorporate amplitude, angular frequency, and phase constant to fully describe the oscillatory behavior.

Simple Harmonic Motion

Simple harmonic motion (SHM) is a type of periodic oscillatory motion where the restoring force is directly proportional to the negative of the displacement. This relationship results in the system oscillating about an equilibrium position in a sinusoidal manner over time.

Amplitude

Amplitude is the maximum displacement of an object from its equilibrium position in oscillatory motion. It represents the extent of the oscillation and indicates the energy of the motion.

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