Question

The displacement \(y\) in centimetre is given in terms of time \(t\) second by the equation \[ y = 3\sin 314t + 4\cos 314t \] The amplitude of SHM is :

• A. 7 cm
• B. 3 cm
• C. 4 cm
• D. 5 cm

Hint:

For combined sine and cosine terms, amplitude is found using Pythagoras.

Answer 1

The Correct Option is D

Concept: For SHM of form: \[ y = a\sin\omega t + b\cos\omega t \] Amplitude: \[ A = \sqrt{a^2 + b^2} \]

Step 1: Identify coefficients.
\[ a = 3, \quad b = 4 \]

Step 2: Calculate amplitude.
\[ A = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{cm} \]