17. Periodic Motion

The historic first playground on Mars has just opened. A child is on a swing with chains of length $2.3\mathrm{m}.$ If a parent pulls the child backward $$ from equilibrium, what is the child's maximum speed? The acceleration due to gravity on Mars is $3.7{\text{m/s}}^2$.

A 20 kg child is on a swing that has chains $2.4\mathrm{m}$ long. Being interested in physics, the child's father gives a push and then watches to see what happens. He notices that the amplitude of the child's oscillation decreases by half in 20 s. What is the value of the time constant?

A 20 kg child is on a swing that has chains $2.4\mathrm{m}$ long. At what frequency should the child's father deliver his pushes to ensure the highest swing possible?

A wooden meter stick is suspended from one end with a frictionless peg. If the meter stick is given a small bump and allowed to oscillate as a pendulum, what is the period of motion?

A simple pendulum 2.00 m long swings through a maximum angle of 30.0° with the vertical. Calculate its period (a) assuming a small amplitude, and (b) using the first three terms of Eq. (14.35). (c) Which of the answers in parts (a) and (b) is more accurate? What is the percentage error of the less accurate answer compared with the more accurate one?

A simple pendulum 2.00 m long swings through a maximum angle of 30.0° with the vertical. Calculate its period (a) assuming a small amplitude, and (b) using the first three terms of Eq. (14.35). (c) Which of the answers in parts (a) and (b) is more accurate? What is the percentage error of the less accurate answer compared with the more accurate one?

A certain simple pendulum has a period on the earth of 1.60 s. What is its period on the surface of Mars, where g = 3.71 m/s^2?

A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light, thin cords 1.50 m long. If a minor earthquake occurs, how many swings per second will these fixtures make?