For a periodic motion represented by the equation y = sinω t + cosω t the amplitude of the motion is

Step-by-step solution

Given the equation of motion is y = sinω t + cosω t       . . . 1 Simplify equation (1) to obtain the standard form: y = 2 sin ω t cos π 4 + cos ω t sin π 4 = 2 sin ω t + π 4       . . . 2 Comparing equation (2) with standard equation of SHM y = A sin ω t + ϕ , we get amplitude of the given oscillation as 2 .