An Initial Amplitude K, Damping Constant C, and Period P $y = k e ^ { - c t } \sin \omega t$

question 94

Essay

An initial amplitude k, damping constant c, and period p are given.
a.) Find a function of the form $y = k e ^ { - c t } \sin \omega t$ that models damped harmonic motion.
b.) Graph the function. $k = 100 , c = 0.5 , p = \frac { \pi } { 12 }$

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Definitions:

Actor-Observer Effect

The tendency to attribute one's own actions to external causes while attributing others' actions to internal factors.

Halo Effect

The cognitive bias that causes one's impression of a person to influence one's thoughts and feelings in unrelated areas.

Mere-Exposure Effect

A psychological phenomenon by which people tend to develop a preference for things or people they are exposed to frequently.

Self-Serving Bias

A cognitive bias that causes individuals to see themselves in a more favorable light, attributing successes to internal factors and failures to external factors.