Question

The period of a pendulum is given by the equation , where is the length of the string suspending the pendulum in meters, and is the acceleration due to gravity in . Which of the following domains provide a real-value period?

1) g > 0
2) g ≥ 0
3) g = 0
4) g < 0

Answer 1

The period of a pendulum has a real value only when the acceleration due to gravity (g) is greater than zero, as the formula for the period includes the square root of l/g.

Step-by-step explanation:

The period T of a simple pendulum is given by the formula T = 2π √(l/g), where l is the length of the string suspending the pendulum and g is the acceleration due to gravity. The period T can only have a real value when the acceleration due to gravity g is greater than zero (g > 0), since the square root of a negative number or zero is not a real number. Thus, the domain for a real-value period for a pendulum is when g > 0.