How to find the amplitude of an object that is in simple harmonic motion?

An object executing simple harmonic motion has a maximum speed of 4.3 m/s and a maximum acceleration of 0.65 m/s^2. Find (a) the amplitude and (b) the period of this motion.How to find the amplitude of an object that is in simple harmonic motion?General "rule of thumb" between the maxima of kinematics quantities of SHM:



vmax = omega*xmax

amax = omega*vmax





To take a maximum of a time derivative...multiply by omega.

To take a maximum of a time integral...divide by omega.



Given that, solve for omega:

omega = amax/vmax



And, thus:

xmax = vmax/omega

xmax= vmax/(amax/vmax)

xmax = vmax^2/amax



Convert omega to a period:

T = 2*Pi/omega



T = 2*Pi*vmax/amax



Summary:

xmax = vmax^2/amax

T = 2*Pi*vmax/amax



Data:

vmax := 4.3 m/s

amax := 0.65 m/s^2



Result:

xmax = 28.4 meters

T = 41.6 seconds