aurelegena

2022-10-07

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time t = 0. amplitude 70 ft, period 0.5 min

Corbin Hanson

Beginner2022-10-08Added 10 answers

Equation of simple harmonic motion for a particle is given .

$$y=A\mathrm{cos}(bt)\phantom{\rule{0ex}{0ex}}A\to \text{Amplitude}\phantom{\rule{0ex}{0ex}}y\to \text{dieplacement}\phantom{\rule{0ex}{0ex}}t\to \text{time}$$

period is given $$\frac{27}{b}=0.5\text{min}\phantom{\rule{0ex}{0ex}}b=\frac{27}{0.5}=47\phantom{\rule{0ex}{0ex}}b=47$$

y=70 cos(47t)

$$y=A\mathrm{cos}(bt)\phantom{\rule{0ex}{0ex}}A\to \text{Amplitude}\phantom{\rule{0ex}{0ex}}y\to \text{dieplacement}\phantom{\rule{0ex}{0ex}}t\to \text{time}$$

period is given $$\frac{27}{b}=0.5\text{min}\phantom{\rule{0ex}{0ex}}b=\frac{27}{0.5}=47\phantom{\rule{0ex}{0ex}}b=47$$

y=70 cos(47t)

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