An object executing simple harmonic motion has a maximum speed of 4.3 m/s and a maximum acceleration of 0.65 m/s2 . find (a) the amplitude and (b) the period of this motion.

(1) The position around equilibrium of an object in simple harmonic motion is described by

where
A is the amplitude of the motion
is the angular frequency.

The velocity is the derivative of the position:

where 
is the maximum velocity of the object.

The acceleration is the derivative of the velocity:

where
is the maximum acceleration of the object.

We know from the problem both maximum velocity and maximum acceleration:


From the first equation, we get
(1)
and if we substitute this into the second equation, we find the angular fequency

while the amplitude is  (using (1)):


(b) We found in the previous step that the angular frequency of the motion is

But the angular frequency is related to the period by

and so, the period is

Answertraveling around a circular trackexplanation"traveling around a circular track" is the best answer as you could be traveling around a circular track at a constant speed. your velocity would therefore have the same magnitude but will always be constantly direction. since acceleration is the rate of change of velocity, the rate of change will only involve the direction of velocity and not the magnitude.wrong choices: "an object at rest" does not accelerate at all"increasing speed while traveling around a curve" means that the acceleration will not be constant due to only change in direction; it will be constant due to both magnitude and direction"an object in free fall" does not necessarily change direction