An object in simple harmonic motion has amplitude 8.0 cm and...

An object in simple harmonic motion has amplitude 8.0 $\mathrm{cm}$ and frequency $0.50 \mathrm{Hz}$ At $t=0$ s it has its most negative velocity. Write the function $x(t)$ that describes the object's position.

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Key Concepts

Phase Shift

Phase shift is a horizontal shift applied to the sinusoidal function to satisfy specific initial conditions, such as the state of velocity or position at t = 0. It adjusts the standard cosine or sine curve so that the model accurately reflects the timing of the maximum or minimum values in the oscillation.

Angular Frequency

Angular frequency represents how fast the oscillation occurs and is given by multiplying the frequency by 2?. It provides a measure in radians per unit time, which is essential when expressing SHM using trigonometric functions.

Simple Harmonic Motion

Simple harmonic motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the negative of the displacement from an equilibrium position. This fundamental concept in oscillatory systems is typically modeled using sinusoidal functions, representing how the system’s position, velocity, and acceleration vary over time.

Amplitude

Amplitude is the maximum displacement of the oscillating object from its equilibrium position. It reflects the energy in the oscillation and is a key parameter in describing the magnitude of the motion in simple harmonic systems.

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