The simple harmonic motion of a particle is given by y = 3 sing co t + 4 cos co t. Which one of the following is the amplitude of such motion?

The given equation for simple harmonic motion (SHM) is y = 3 sin ωt + 4 cos ωt. This is a linear combination of two perpendicular SHMs or a sine and cosine function of the same frequency. For any SHM expressed in the form y = A sin ωt + B cos ωt, the resultant motion is also simple harmonic with a resultant amplitude (R) calculated using the Pythagorean theorem: R = √(A² + B²) [t1][t6]. In this specific case, A = 3 and B = 4. Therefore, the amplitude is √(3² + 4²) = √(9 + 16) = √25 = 5 [t4][t9]. This mathematical approach treats the coefficients as vector components or phasors where the sine and cosine terms are 90 degrees (π/2) out of phase [t1][t2]. Thus, the amplitude of the particle's motion is 5 units.