17. Periodic Motion

A 280-kg wooden raft floats on a lake. When a 68-kg man stands on the raft, it sinks 3.5 cm deeper into the water. When he steps off, the raft oscillates for a while. What is the frequency of oscillation?

(II) A 1.45-kg mass stretches a vertical spring 0.245 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?

A wood block of mass 52 g floats on a lake, bobbing up and down at a frequency of 3.5 Hz. A partially filled water bottle of mass 0.28 kg and almost the same size and shape of the wood block is tossed into the water. At what frequency would you expect the bottle to bob up and down? Assume SHM.

A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30 oscillations in 20 s, what are its (a) mass and (b) maximum speed?

A spring is hanging from the ceiling. Attaching a 500 g physics book to the spring causes it to stretch 20 cm in order to come to equilibrium. From equilibrium, the book is pulled down 10 cm and released. What is the period of oscillation?

A 200 g block hangs from a spring with spring constant 10 N/m. At t = 0 s the block is 20 cm below the equilibrium point and moving upward with a speed of 100 cm/s. What are the block's a. Oscillation frequency?

(II) Estimate the spring constant in a child’s pogo stick if the child has a mass of 32 kg and bounces once every 1.6 seconds.

A compact car has a mass of 1200 kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs. What will be the car's oscillation frequency while carrying four 70 kg passengers?

A fisherman’s scale stretches 3.2 cm when a 2.4-kg fish hangs from it. What will be the amplitude and frequency of oscillation if the fish is pulled down 2.1 cm more and released so that it oscillates up and down?

(II) A block of mass m is supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 14–31). What will be the frequency of vertical oscillation?

A 1.60-kg object oscillates at the end of a vertically hanging light spring once every 0.68 s. Assume the spring was initially compressed 16 cm from the equilibrium position (where y = 0 ), and then (t = 0) was released. What will be its maximum acceleration, and where will it first be attained?

(III) A uniform 1.25-m-long stick of mass M can rotate easily about a hinge at one end and is held horizontal by a spring with spring constant k attached at the other end (Fig. 14–32). If that end of the stick oscillates up and down slightly, what is its frequency? [Hint: Write a torque equation about the hinge.]

Scientists are measuring the properties of a newly discovered elastic material. They create a 1.5-m-long, 1.6-mm-diameter cord, attach an 850 g mass to the lower end, then pull the mass down 2.5 mm and release it. Their high-speed video camera records 36 oscillations in 2.0 s. What is Young's modulus of the material?