In the equation of a particle vibrating in Simple Harmonic Motion (SHM) given as 2y = 8sin(4πt), we can determine the amplitude and angular frequency from the equation.
The general equation for SHM is y = A*sin(ωt + φ), where A represents the amplitude, ω represents the angular frequency, t is the time, and φ is the phase constant.
Comparing the given equation 2y = 8sin(4πt) with the general equation, we can see that:
Amplitude (A) = 8/2 = 4
The amplitude is half the coefficient of the sine term, which in this case is 8 divided by 2.
To find the angular frequency (ω), we can use the relation ω = 2πf, where f is the frequency. In this case, the coefficient of 't' in the given equation is 4π, which corresponds to 4π radians per unit of time.
Angular frequency (ω) = 4π
Therefore, the amplitude of the motion is 4 units, and the angular frequency is 4π radians per unit of time.