Ascience 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

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y