A mass oscillates up and down on a vertical spring with an amplitude of 6 cm and a period of 2 s. What total distance does the mass travel in 16 seconds?
To find the total distance traveled by the mass in 16 seconds, we need to determine how many complete oscillations occur within that time period.
Given that the period of oscillation is 2 seconds, we can calculate the number of complete oscillations by dividing the total time (16 seconds) by the period:
Number of complete oscillations = Total time / Period
= 16 s / 2 s
= 8
Since each complete oscillation involves the mass traveling from its highest point to its lowest point and then back to the highest point, the total distance traveled within one complete oscillation is twice the amplitude.
Total distance traveled in 8 complete oscillations = 2 * Amplitude * Number of complete oscillations
= 2 * 6 cm * 8
= 96 cm
Therefore, the mass travels a total distance of 96 cm in 16 seconds.