Question

For a periodic motion represented by the equation y = sin ωt + cos ωt, the amplitude of the motion is

• A. \(\sqrt 2\)
• B. 1
• C. 2
• D. 0.5

Answer 1

The Correct Option is A

The equation of motion for simple harmonic motion (SHM) is given by: \[ y = A \sin(\omega t) + B \cos(\omega t) \] The amplitude of the motion is given by: \[ \text{Amplitude} = \sqrt{A^2 + B^2} \] Here, \( A = 1 \) and \( B = 1 \) in the equation \( y = \sin(\omega t) + \cos(\omega t) \). Therefore, the amplitude is: \[ \text{Amplitude} = \sqrt{(1)^2 + (1)^2} = \sqrt{2} \] Thus, the amplitude is \( \sqrt{2} \).