In simple harmonic motion (SHM), the maximum velocity occurs when the body is at its maximum displacement from the equilibrium position. The relationship between the maximum velocity (Vmax), angular frequency (ω), and amplitude (A) of SHM is given by the equation:
Vmax = ωA
The angular frequency (ω) is related to the frequency (f) by the equation:
ω = 2πf
Given that the frequency is 60 Hz, we can calculate the angular frequency as follows:
ω = 2π(60 Hz) = 120π rad/s
The amplitude (A) is given as 2 cm. However, it's important to convert the amplitude to meters before calculating the maximum velocity. Since 1 meter is equal to 100 centimeters, the amplitude in meters is:
A = 2 cm = 2/100 m = 0.02 m
Now, we can substitute the values into the equation for Vmax:
Vmax = (120π rad/s) (0.02 m) = 2.4π m/s
Therefore, the maximum velocity of the body in terms of π is 2.4π m/s.