Simple Harmonic Motion

You need to know the height of a tower, but darkness obscures the ceiling.

You note that a pendulum extending from the ceiling almost touches the

floor and that its period is 24 s. How tall is the tower?

L = T²ag ÷ 4π²

• 1.1 x 10² m

• 1.4 x 10² m

• 5 x 10² m

• 3.2 x 10² m

You are designing a pendulum clock to have a period of 1.0 s.

How long should the pendulum be?

L = T²ag ÷ 4π²

• 2.5 cm

• 5 cm

• 25m

• 25 cm

A trapeze artist swings in simple harmonic motion with a period of 3.8 s.

Calculate the length of the cables supporting the trapeze.

L = T²ag ÷ 4π²

• 36 cm

• 28 cm

• 3.6 m

• 2.8 m

Calculate the period and frequency of a 3.500 m long pendulum at the

North Pole, where ag = 9.832 m/s²

T = 2π √ L/ag

f = 1 / T

• 3.754 s, 0.2664 Hz

• 3.749 s, 0.2667 Hz

• 3.758 s, 0.2661 Hz

• 2.8 m3.749 s, 0.2661 Hz

Calculate the period and frequency of a 3.500 m long pendulum at Chicago, where ag = 9.803 m/s²

T = 2π √ L/ag

f = 1 / T

• 3.754 s, 0.2664 Hz

• 3.749 s, 0.2667 Hz

• 3.758 s, 0.2661 Hz

• 2.8 m3.749 s, 0.2661 Hz

Calculate the period and frequency of a 3.500 m long pendulum at Jakarta, Indonesia, where ag = 9.782 m/s²

T = 2π √ L/ag

f = 1 / T

• 3.754 s, 0.2664 Hz

• 3.749 s, 0.2667 Hz

• 3.758 s, 0.2661 Hz

• 2.8 m3.749 s, 0.2661 Hz