Question

The displacement of a particle executing SHM is given by y = 10 sin (6t + $\frac{\pi}{3}$) m where t is in seconds. The initial displacement and velocity of the particle are respectively

• A. 5√3 m and 30 m/s
• B. 15 m and 5√3m/s
• C. 15√3 m and 30 m/s
• D. 10√3 m and 30 m/s

Answer 1

Answer: (B)

15 m and 5√3m/s

Answer 2

y = 10 sin (6t + π/3)

At t = 0,

y = 10 sin $\frac{\pi}{3} = \frac{10\sqrt{3}}{2}$m. = 5$\sqrt{3}$ m

v = $\frac{dy}{dt} = 10 \times 6$cos(6t + $\frac{\pi}{3}$) = 60 cos (6t + $\frac{\pi}{3}$)

At t = 0

v = 60 cos $\frac{\pi}{3}$ = $\frac{60}{2}$ = 30 m/s