A particle in simple harmonic motion has an angular frequency of 24 rad/s. Its maximum velocity is 25 m/s. What is its maximum acceleration?

The basic equation of motion for harmonic motion is:


x(t) = A \sin(\omega t)


You have been given the value for \omega. Now take the derivative of this to find the particle's velocity:


v(t) = \frac {dx}{dt} = A \omega \cos (\omega t)


You have been given the max value of its velocity, so you can now determine the value for A.

The equation for acceleration is the derivative of the velocity equation - you can do the math and determine its maximum value. Post back with what you get and we'll check it for you.