A pendulum swings with a period of 1 second. If the length of the pendulum is increased by a factor of 4, what will be the new period?

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Q: A pendulum swings with a period of 1 second. If the length of the pendulum is increased by a factor of 4, what will be the new period?

Solution: The period T = 2π√(L/g). If L is increased by a factor of 4, T increases by a factor of √4 = 2.

Steps: 6

Step 1: Understand that the period of a pendulum (T) is related to its length (L) using the formula T = 2π√(L/g), where g is the acceleration due to gravity.
Step 2: Note that the original period of the pendulum is 1 second, which means we can use this to understand the relationship between length and period.
Step 3: Recognize that if the length of the pendulum is increased by a factor of 4, we can express the new length as L' = 4L.
Step 4: Substitute the new length into the period formula: T' = 2π√(L'/g) = 2π√(4L/g).
Step 5: Simplify the equation: T' = 2π√(4) * √(L/g) = 2 * (2π√(L/g)) = 2 * T.
Step 6: Since the original period T is 1 second, the new period T' will be 2 * 1 second = 2 seconds.