A weight suspended from a spring is seen to bob up and down over a distance of 50 centimeters 2 times each second. What is its frequency? What is its period? What is its amplitude?
To find the frequency, period, and amplitude of a weight suspended from a spring bobbing up and down, we can use the following formulas:
1. Frequency (f) = number of oscillations per unit time.
Frequency (f) = 2 / period (T)
2. Period (T) = time taken for one complete oscillation.
Period (T) = 1 / frequency (f)
3. Amplitude (A) = maximum displacement from the mean position.
Given that the weight bobs up and down over a distance of 50 centimeters (or 0.50 meters) twice each second, we can apply these formulas.
Frequency (f) = 2 / period (T)
If it bobs twice each second, the number of oscillations per second is 2 (since each bobbing up and down counts as one oscillation).
So, the frequency (f) = 2 Hz.
Period (T) = 1 / frequency (f)
Using the frequency value we found earlier, we can calculate the period.
Period (T) = 1 / 2
Thus, the period (T) = 0.5 seconds.
Amplitude (A) = maximum displacement from the mean position
Given the distance it bobs up and down is 50 centimeters (or 0.50 meters), the amplitude is half of this distance.
So, the amplitude (A) = 0.25 meters.
Therefore, the frequency is 2 Hz, the period is 0.5 seconds, and the amplitude is 0.25 meters.