Find the displacement and the velocity of the particle

Question

The displacement of a particle in centimetres is given by y=8 sin (2πft). If f=20 Hz, find the displacement and the velocity of the particle at a time t=0.01 s and 0.07 s.

Answer 1

y = 8 sin (2*pi*f*t), f = 20 Hz

y(0.01 s) = 8 sin (2*pi*20*0.01) cm = 7.608 cm

y(0.07 s) = 8 sin (2*pi*20*0.07) cm = 4.702 cm

y_dot = 16*pi*f cos (2*pi*f*t)

y_dot(0.01 s) = 16*pi*20 cos (2*pi*20*0.01) = 310.7 cm/s

y_dot(0.07 s) = 16*pi*20 cos (2*pi*20*0.07) = -813.3 cm/s