Answer:
The period of a spring-mass system is the time it takes for the weight to complete one full cycle of motion (i.e., go up and down once).
In this problem, we are told that the weight goes up and down 60 times in 90 seconds. Therefore, the time it takes for the weight to complete one cycle of motion is:
90 seconds / 60 cycles = 1.5 seconds/cycle
To find the period of the motion in minutes, we need to convert the time per cycle from seconds to minutes:
1.5 seconds/cycle * 1 minute/60 seconds = 0.025 minutes/cycle
Therefore, the period of the motion is 0.025 minutes/cycle or 25 milliseconds/cycle. In this case, it is 1/40 minutes.