Answer:
The first occurence of t for which x = 0 is t = 0.5.
Step-by-step explanation:
The harmonic motion is described by the following equation.
[tex]x(t) = 3\cos{\pi t}[/tex]
What is the first occurrence of a value of t for which x = 0?
This is t when [tex]x(t) = 0[/tex]. So
[tex]x(t) = 3\cos{\pi t}[/tex]
[tex]3\cos{\pi t} = 0[/tex]
[tex]\cos{\pi t} = \frac{0}{3}[/tex]
[tex]\cos{\pi t} = 0[/tex]
The inverse of the cosine is the arcosine. So we apply the arcosine function to both sides of the equality.
[tex]\arccos{\cos{\pi t}} = \arccos{0}[/tex]
[tex]\pi t = \frac{\pi}{2}[/tex]
[tex]t = \frac{\pi}{2 \pi}[/tex]
[tex]t = \frac{1}{2}[/tex]
[tex]t = 0.5[/tex]
The first occurence of t for which x = 0 is t = 0.5.
