Pendulum question-Last minute physics homework help needed!

Question

In a science museum, you may have seen a Foucault pendulum, which is used to demonstrate the rotation of the earth. In one museum's pendulum, the 110 kg bob swings from a 17.4-m-long cable with an amplitude of 5.5 ∘.

1. What is the period of this pendulum?
2. What is the bob's maximum speed?
3. What is the pendulum's maximum kinetic energy?
4. When the bob is at its maximum displacement, how much higher is it than when it is at its equilibrium position?

Answer 1

Period T = 2π√l/g = 2π√(17.4m/9.81m/s²) = 8.368 s

Maximum speed: max v from equation mv²/2 = mgh = mgl(1 - cos5.5°); v = √2gl(1 - cos5.5°) = √2·9.81m/s²·

17.4m(1 - cos5.5°) = 1.254 m/s

Maximum kinetic energy: K = mv²/2 = 110kg·1.254²m/s²/2 = 86.488 J

Maximum height: H = l(1 - cos5.5°) = 17.4m(1 - cos5.5°) = 0.080 m