Question

The equation of motion of a particle undergoing simple harmonic motion is x=4.00sin0.500t, where x is in centimeters. At t=1.00 s, determine the particle's displacement, velocity, and acceleration.

Answer 1

hiven 4.00 Sin (0.500t) X2 v-dx0 Cos Co.st) dt dk Sin (0.5t) No At t I.oos, > /v = 1.99 cm) a Sin (o. 5x)

Answer 2

SOLUTION :

Given :

x = 4.00 sin (0.500 t) 

So, 

Displacement x,  at t = 1.00 s is :

= 4.00 sin (0.500 * 1.00) 

= 1.92 cm (ANSWER).

Velocity v(t) = d/dt(4.00 sin (0.500 t)) = 4.00 * 0.500 cos(0.500 t)

=> v(1.00) = 2.00 cos(0.500 * 1.00)

=> v(1.00) = 1.7555 cm/s (ANSWER).

Acceleration a(t) = d/dt(2.00 cos (0.500 t)) = - 2.00 * 0.500 sin (0.500 t)

=> a(1.00) = - 1.00 sin (0.500 * 1.00)

=> a(1.00) = - 0.48 cm/s^2 (ANSWER).