Question Detail
Question
The displacement x in meters at t = 0 (x0) for a S.H.M. given by the equation x = 3sin3πt + 4cos3πt is
Correct Answer
Option D is the correct answer.
Detailed Explanation
The displacement equation for Simple Harmonic Motion (S.H.M.) is given as: x(t) = 3sin(3πt) + 4cos(3πt).To find the displacement at t = 0 (x0), substitute t = 0 into the equation:x(0) = 3sin(3π × 0) + 4cos(3π × 0)x(0) = 3sin(0) + 4cos(0)We know that sin(0) = 0 and cos(0) = 1.x(0) = 3(0) + 4(1)x(0) = 0 + 4x(0) = 4 m.
Hint
Simply substitute t=0 into the given displacement equation and evaluate the trigonometric functions.