Question

particle if \( t =\frac{ T }{4} \) is taken as starting time is (Notations have usual meanings) (A) \( A \sin \left(\omega t+\frac{2 \pi}{3}\right) \) (B) \( A \sin \left(\omega t+\frac{\pi}{3}\right) \) (C) \( A \sin \left(\omega t+\frac{\pi}{6}\right) \) (D) \( A \cos \left(\omega t+\frac{2 \pi}{3}\right) \) SH0043

Answer 1

(B) \( A \sin \left(\omega t+\frac{\pi}{3}\right) \)

Explanation:

At \( t = \frac{T}{4} \), the particle is at a positive extreme. Therefore, the equation of the particle is given by:

$$x = A \sin \left(\omega t + \frac{\pi}{3}\right)$$

Hence, the correct answer is (B) \( A \sin \left(\omega t+\frac{\pi}{3}\right) \).

Note: The other options are incorrect because they either have the wrong phase angle or the wrong trigonometric function.