An spring has a period of 4 seconds. What is its frequency? A pendulum has a frequency of 3 Hz . What is its period? A pendulum takes 10 seconds to complete 2 cycles. A) What is its period? B) What is its frequency?

To find the frequency of a spring with a period of 4 seconds, you use the formula \( f = \frac{1}{T} \), where \( T \) is the period. So, \( f = \frac{1}{4} = 0.25 \) Hz. For the pendulum, the period can be calculated using the same formula. Since the frequency is 3 Hz, the period \( T = \frac{1}{3} \approx 0.33 \) seconds. For the pendulum that takes 10 seconds to complete 2 cycles, you can find the period by dividing the total time by the number of cycles. Thus, \( T = \frac{10}{2} = 5 \) seconds. To find its frequency, use \( f = \frac{1}{T} \); hence, \( f = \frac{1}{5} = 0.20 \) Hz. Did you know that the period of a pendulum is largely influenced by its length? The longer the pendulum, the slower it swings, leading to a longer period. This principle is why pendulum clocks were so effective – they could be calibrated for precise timekeeping! For those curious about sound waves and musical instruments, the frequency of a sound wave determines its pitch. Higher frequencies correspond to higher notes, like a piccolo, while lower frequencies produce deeper sounds, like a tuba. So every time you strike a note, remember, it's all about those cycles per second!