To solve this problem it is necessary to apply the concepts related to the simple harmonic movement, to the speed in terms of displacement and the timpo, as well as the angular frequency and the period of frequency.
PART A) According to the description given, 5 revolutions are made in one minute (or 60 seconds) that is to say that the frequency would be given by
[tex]f = \frac{1}{12s^{-1}}[/tex]
Therefore the angular velocity can be found as
[tex]\omega = 2\pi f[/tex]
[tex]\omega = 0.52rad/s[/tex]
The displacement that determines the maximum displacement based on the angular velocity time and the time in the simple harmonic movement, is equal to the radius of the circle, in other words
[tex]x = Acos(\omega t)[/tex]
Where,
A = Amplitude
[tex]\omega =[/tex] Angular velocity
t = time
If for our given values the value of the amplitude is 2m and the value of the angular velocity is 0.52rad/s
[tex]x = 2cos(0.52t)[/tex]
So the equation for the position of the shadow is of
[tex]x(t) = 2cos(0.52t)[/tex]
PART B) The equation for the velocity of the shadow is calculated as a expression of the displacement against the time, if we differenciate the previous value found, we have that,
[tex]\frac{dx}{dt} = \frac{d(2cos(0.52t))}{dt}[/tex]
[tex]v(t) = 2(-0.52)sin(0.523t)[/tex]
[tex]v(t) = -1.05sin(0.52t)[/tex]
