A science museum has asked you to design a simple pendulum that will make 29.0 complete swings in 83.0 s. What length should you specify for this pendulum?

2.035 m

Explanation:

The period of oscillation in a simple pendulum when the angle of swing is not too large relates to the length with the formula:

T = 2π√ (L/g) where L is the length of the pendulum in meters, T is the period in seconds, and g is acceleration due to gravity in m/s^2

T can be calculated by

T = time of oscillations / number of complete oscillations (complete swings)

T = 83/29 = 2.862s

Deriving an equation for L

T = 2π √ (L/g)

Divide both side by 2π

T / 2π = √ (L/g)

Square both sides

T^2/4π^2 = L/g

Cross multiply

T^2 * g / 4π^2

Substitute in the values of the terms

(2.862^2) * 9.81 / (4 * 3.142 * 3.142) = 2.035m