Answer:
1/2 Hz
Explanation:
A simple harmonic motion has an equation in the form of
[tex]x(t) = Acos(\omega t - \phi)[/tex]
where A is the amplitude, [tex]\omega = 2\pi f[/tex] is the angular frequency and [tex]\phi[/tex] is the initial phase.
Since our body has an equation of x = 5cos(π t + π/3) we can equate [tex]\omega = \pi[/tex] and solve for frequency f
[tex]2\pi f = \pi[/tex]
f = 1/2 Hz
0.5Hz
The general equation of the displacement, x, of a body undergoing simple harmonic motion at a given point in time (t) is given by;
x = A cos (ωt ± ∅) --------------------------(i)
where;
A = amplitude of the wave
ω = angular velocity of the wave
∅ = phase constant of the wave
From the question;
x = 5cos(π t + π/3) -----------------------------(ii)
Comparing equations (i) and (ii), the following deductions among others can be made;
A = 5cm
ω = π
But the angular velocity (ω) of the wave is related to its frequency (f) as follows;
ω = 2 π f --------------------(iii)
Substitute the value of ω = π into equation (iii) as follows;
π = 2 π f
Divide through by π;
1 = 2f
Solve for f;
f = 1/2
f = 0.5
Frequency (f) is measured in Hz. Therefore, the frequency of the oscillation is 0.5Hz
