Question

1. (I) A body oscillates with simple harmonic motion according to the equation:
x = (2.0cm) cos[(π/3 rad/s)t − π/6 rad] .
What are (a) the displacement, (b) the velocity, and (c) the acceleration at time t = 3.0s? Find also (d) the frequency and (e) the period of oscillation. 1. (I) A body oscillates with simple harmonic motion according to the equation:
x = (2.0cm) cos[(π/3 rad/s)t − π/6 rad] .
What are (a) the displacement, (b) the velocity, and (c) the acceleration at time t = 3.0s? Find also (d) the frequency and (e) the period of oscillation. @Physics

Answer 1

if x(t) defines position; then x'(t) defines velocity at any given time.

\[x' = -\frac{2pi}{3}\ sin(\frac{pi}{3}t-\frac{pi}{6})\]

just calculate it at t=3 for its instantaneous velocity

Answer 2

displacment is the difference between x(0) and x(3)

Answer 3

acceleration is the rate of change in velocity, so we can derive x'(t) to get it:

\[x''= -\frac{2(pi)^2}{9}\ cos(\frac{pi}{3}t-\frac{pi}{6})\]