Question

in a physics lab you studied the oscillations of a pendulum. if a pendulum makes 48 complete cycles in 12 seconds. find the period.

Explanation:

Step1: Recall the formula for period

The period \( T \) of a pendulum (or any oscillating object) is the time taken for one complete cycle. The formula relating the number of cycles \( n \), total time \( t \), and period \( T \) is \( T=\frac{t}{n} \).

Step2: Identify the given values

We are given that the number of complete cycles \( n = 48 \) and the total time \( t=12 \) seconds.

Step3: Substitute the values into the formula

Substitute \( t = 12 \) seconds and \( n=48 \) into the formula \( T=\frac{t}{n} \). So, \( T=\frac{12}{48} \).

Step4: Simplify the fraction

Simplify \( \frac{12}{48} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 12. \( \frac{12\div12}{48\div12}=\frac{1}{4} = 0.25 \) seconds.

Answer:

The period of the pendulum is \( 0.25 \) seconds.