The displacement of a body executing SHM is given by x = A sin (2πt + π/3). The first time from t = 0 when the velocity is maximum is.
Physics · Simple Harmonic Motion
JEE Mains Advanced

Question

The displacement of a body executing SHM is given by x = A sin (2πt + π/3). The first time from t = 0 when the velocity is maximum is.

G1 Physics · Accepted Answer

x=A sin(2πt+π/3), so v=2πA cos(2πt+π/3). Velocity is maximum positive when the phase first becomes 2π. Thus 2πt+π/3=2π ⇒ t=5/6 s; the maximum magnitude of velocity first occurs when cos=−1 at phase π: 2πt+π/3=π ⇒ t=1/3 s≈0.33 s. Source answer: 0.33 s.