Question

A pendulum of unknown mass is attached to the ceiling and nearly touches the floor as it completes 6 full cycles in 45 s. At its lowest point, the pendulum moves at a speed of 4.15 m/s.
part a. What is the height of the ceiling?
part b. What is the maximum height of the pendulum?
part c. If the pendulum were moved to the moon, with a gravitational acceleration of 1.62 m/s2, what would be the resulting frequency?
part d. If the pendulum, back on Earth, were raised to a height of 0.22 m and released, what would be the resulting frequency of the motion?

Answer 1

Answer:

a) h = 14 m

b) h = 88 cm

c) f = 0.054 Hz

d) f = 0.13 Hz

Explanation:

a) T = 2π√(L/g)

L = T²g/4π²

L = (45/6)²(9.8) / 4π² = 13.963...

b) ½mv² = mgh

h = v²/2g

h = 4.15²/ (2(9.8)) = 0.87869

c) f = 1/T = 1 / (2π√(14 / 1.62)) = 0.0542

d) f = 6/45 = 0.13333...