Question

The length of time that it takes for a pendulum to make one complete swing depends on the length of the pendulum. The time in seconds, T, is related to the length in metres, L, through the equation T=2π√ L/9.8

Write this equation in function notation. (1 mark)
State the domain and range of this function. (1 mark)
Graph this function for pendulums up to 20m in length. (3 marks)
If you wanted to construct a pendulum in the Ontario Science Centre that takes exactly 10s to complete one swing, how long would it have to be (to the nearest millimetre)? (2 marks)
What would be the effect on the value of T if the pendulum were made twice as heavy? (1 mark)

Answer 1

T(L) = 2π√(L/9.8)

10 = 2π√(L/9.8)
5/π = √(L/9.8)
25/π^2 = L/9.8
L = 25(9.8)/π^2 = 24.824 m or 24824 mm

change in mass has no effect