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The table provided by the problem helps you to find the amplitude, period and vertical translation.
Notice that the maximum height is of 55 meters and the minimum height is of 5 meters, hence, you may evaluate the peak-to-peak amplitude such that:
`2A = 55 - 5 => A = 50/2 => A = 25 ` meters
According to the given table, it takes 7 seconds to reach the lowest point, hence, the complete period of time is of 2*7 = 14 seconds.
You need to remember the equations that relates the frequency, angular frequency and the period such that:
`T = 1/f`
`f = omega/(2pi) => T = 1/(omega/(2pi)) => T = 2pi/omega`
`omega = 2pi/T`
Since T = 14 seconds, you need to substitute 14 for T in equation above such that:
`omega = 2pi/14 => omega = pi/7`
You need to put the equation in the form `h(t) = asin[b(t - c)] + d` , hence, you need to substitute 25 for a, `pi/7` for b and you need to evaluate the vertical translation d such that:
`d = (55 + 5)/2 => d = 30`
`h(t) = 25sin(pi/7(t - c)) + 30`
Hence, evaluating the equation of the function in the form `h(t) = asin[b(t - c)] + d` yields`h(t) = 25sin(pi/7(t - c)) + 30.`
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