∙If the displacement of an oscillator in SHM is described by...

$\bullet$ If the displacement of an oscillator in SHM is described by the equation $y=(0.25 \mathrm{~m}) \cos [(314 \mathrm{rad} / \mathrm{s}) t],$ where $y$ is in meters and $t$ is in seconds, what is the position of the oscillator at (a) $t=0,$ (b) $t=5.0 \mathrm{~s},$ and $(\mathrm{c}) t=15 \mathrm{~s} ?$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Simple Harmonic Motion

Simple Harmonic Motion (SHM) is a type of periodic motion in which the restoring force is directly proportional to the displacement from an equilibrium position and acts in the opposite direction. This fundamental concept describes many physical systems that oscillate back and forth in a regular, sinusoidal pattern.

Amplitude

Amplitude is the maximum displacement from the equilibrium position in an oscillatory system. It quantifies the extent of the oscillation and is a key parameter in determining the energy of the motion.

Angular Frequency

Angular frequency, measured in radians per second, describes how fast the oscillator completes its cycle. It is intrinsically linked to the period of oscillation and directly influences the rate at which the sine or cosine function cycles through its values.

Displacement Equation in SHM

The displacement of an oscillator in SHM is typically represented by an equation of the form y = A cos(?t + ?), where A is the amplitude, ? is the angular frequency, t is the time, and ? is the phase constant. This equation models the time-dependent behavior of the oscillator, allowing for the determination of its position at any given moment.

Transcript

Please give Ace some feedback