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?
Doesn't it may 8 cycles? Each cycle is down and up, or 24cm.
To find the total distance the mass travels in 16 seconds, we first need to determine the number of complete periods the mass undergoes in that time.
We are given that the period of the oscillation is 2 seconds. The total time of 16 seconds can be divided into 8 complete periods (16/2 = 8).
Now, we know that the mass oscillates up and down with an amplitude of 6 cm. The total distance covered by the mass in one complete period is twice the amplitude (since it travels up and down).
Therefore, the total distance traveled by the mass in one complete period is 2 × 6 cm = 12 cm.
Since the mass undergoes 8 complete periods in 16 seconds, the total distance traveled by the mass in 16 seconds is 8 × 12 cm = 96 cm.
Therefore, the mass travels a total distance of 96 cm in 16 seconds.