what is the acceleration of the body at a certain time?

Question

A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation:

x(t) = A sin(W t + phi)

If A = 3 m, W= 2.999 rad/s, and phi = 1.0472 rad, what is the acceleration of the body at t = 3 s?

Note: The argument of the sine function is in radians rather than degrees. Answer in units of m/s^2.

Answer 1

The displacement is x(t) = A sin(W t + phi)
We have to use a little Calculus
Instantaneous velocity is v(t)=x'(t)= A W cos(W t + phi)
Instantaneous acceleration is a(t)=x''(t)=-A W^2 sin(W t + phi)


so
a(3)= - (3)(2.999)^2 sin(2.999 (3) + 1.0472 )=
a(3)= 15.67m/sec^2