Question

find a model for simple harmonic motion if the position at t=0 is 0 the amplitude is 3 centimeters and the period is 2 seconds

Answer 1

So our model could be formed using these:

The amplitude (\(3\)) accounts for a multiplier on the sin/cos/tan
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\(f(t)=\color{tomato}{3}(t)\)
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Our position, \(t=0\) at \(0\), gives us a \((0,0)\), which, with the multiplier (\(3\)), is still \((0,0\) — \((0,0 \times 3) = (0,0)\), this would give us a sine curve
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\(f(t)=\color{tomato}{3}\color{lime}{sin}(t)\)
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If the period was 0, the \((t)\) wouldn’t be affected, but the period is 2, so we have to work it out using this equation:
\(\dfrac{2 \pi}{b} = 2\)
(Multiply both sides by b)
\(2 \pi = 2b\)
(Divide both sides by 2)
\(\dfrac{2\pi}{2}=b\)
(Simplify)
\(\pi = b\)
This would leave you with what your period value is, \(\pi\)
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\(f(t)=\color{tomato}{3}\color{lime}{sin}(\color{cyan}{\pi} t)\)
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