A damped harmonic oscillator's displacement from equilibrium is described by the equation x ( t ) = 4 e − 0.5 t cos ⁡ ( 4 t ) x(t)=4e^{-0.5t}\cos(4t) , where t t is time in seconds. Find the first time at which the oscillator's displacement is at a maximum.

t = 0.754 seconds t=0.754\text{ seconds}

t = 2.754 seconds t=2.754\text{ seconds}

t = 1.754 seconds t=1.754\text{ seconds}

t = 0.457 seconds t=0.457\text{ seconds}

6. Graphical Applications of Derivatives - Part 2 of 2

6. Graphical Applications of Derivatives / Applied Optimization / Problem 7

Problem 7

A damped harmonic oscillator's displacement from equilibrium is described by the equation $x (t) = 4 e^{- 0.5 t} \cos (4 t)$ , where $t$ is time in seconds. Find the first time at which the oscillator's displacement is at a maximum.

$t equals 2.754 seconds$

$t equals 0.754 seconds$

$t equals 1.754 seconds$

$t equals 0.457 seconds$