Step-by-step explanation:
The equation 2y = 8 sin (4πt) is a general equation for a particle vibrating in simple harmonic motion. The amplitude of the oscillations is given by the coefficient of the sine term, which is 8 in this equation. Therefore, the amplitude of the particle vibrating in simple harmonic motion is 8 cm.
The angular frequency is given by the coefficient of the variable t, which is 4π in this equation. Therefore, the angular frequency of the particle vibrating in simple harmonic motion is 4π rad/s.
Therefore, the answer is (b) 4 cm and 4π rad.