Question Detail
Question
If the displacement of a moving particle is given by x = 5cos ωt + 12sin ωt, what is the amplitude of the motion?
Correct Answer
Option C is the correct answer.
Detailed Explanation
From Worked Example 42 (page 44) or the 'Alternative Mathematical Expressions for SHM' section (page 3, Equation 6), if x(t) = C cos ωt + D sin ωt, then the amplitude A is given by A = √(C² + D²). Here, C = 5 and D = 12. So, A = √(5² + 12²) = √(25 + 144) = √169 = 13 units.
Hint
Recall the formula for amplitude when the SHM equation is expressed as a sum of sine and cosine functions. Refer to the 'Generalized Mathematical Expressions for SHM' or 'Alternative Mathematical Expressions for SHM' section on pages 2-3.