17. Periodic Motion

You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. How much time does it take the pendulum bob to reach its highest speed?

A plywood disk of radius 20.0 cm and mass 2.20 kg has a small hole drilled through it, 2.00 cm from its edge (Fig. 14–38). The disk is hung from the wall by means of a metal pin through the hole, and is used as a pendulum. What is the period of this pendulum for small oscillations?

A pendulum is made by tying a 75 g ball to a 130-cm-long string. The ball is pulled 5.0° to the side and released. How many times does the ball pass through the lowest point of its arc in 7.5 s?

A simple pendulum oscillates with frequency ƒ. What is its frequency if the entire pendulum accelerates at 0.35 g upward?

What is the period of a simple pendulum 47 cm long when it is in a freely falling elevator?

A simple pendulum is made from a $0.65m$ long string. What is the period of its oscillation near Earth's surface (assume $g=9.8m/s^2$)?

A uniform rod of mass M and length L swings as a pendulum on a pivot at distance L/4 from one end of the rod. Find an expression for the frequency f of small-angle oscillations.

The length of a simple pendulum is 0.72 m, the pendulum bob has a mass of 295 g, and it is released at an angle of 12° to the vertical. Assume SHM. With what frequency does it oscillate?

(II) The human leg can be compared to a physical pendulum, with a “natural” swinging period at which walking is easiest. Consider the leg as two rods joined rigidly together at the knee; the axis for the leg is the hip joint. The length of each rod is about the same: assume 55 cm. Let the upper rod have a mass of 7.0 kg and the lower rod a mass of 4.0 kg. Calculate the natural swinging period of the system.

You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. How much time does it take if the pendulum is released at an angle of 1.75° instead of 3.50°?

For a simple pendulum undergoing simple harmonic motion, at which position is the acceleration of the pendulum bob equal to $0$?

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/s²?

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?