A mass on a spring undergoes simple harmonic motion with amp

A mass on a spring undergoes simple harmonic motion with amplitude A. In a time equal to three periods, what is the magnitude of the displacement of the mass? In a time equal to three periods, what actual distance did it travel?

Solution

a. At the end of each time period, the mass comes back to its original position. Displacement at the end of each period is equal to zero

Hence, magnitude of the displacement of the mass in a time equal to three periods, displacement = 0 units.

b. Distance travelled by the mass in each time period, s = 4A units

Hence the distance travelled in three time periods

Distance = 3 X s

= 3 X 4A

Distance = 12A units