If the pendulum swings out to its widest position in 2 seconds, model the horizontal displacement of the pendulum using a sinusoidal function, considering vertical to be x = 0.

Question

A pendulum is connected to a rope 3 m long, which is connected to a ceiling 4 m high. The angle between its widest swing and vertical hanging position is . If the pendulum swings out to its widest position in 2 seconds, model the horizontal displacement of the pendulum using a sinusoidal function, considering vertical to be x = 0.

Grade 12 Advanced Functions

Please write clearly and neatly. Thanks

Answer 1

pendulum has period of 8s.

2+2+2+2=8

1/P=f/2π,,,,P=perioid, f=frequency

f=π/4

at θ=π/3 x=3*sin(π/3)=3√3

x=(3√3)*sin(πt/4)

check t=0, t=2, t=4, t=6 t=8