17. Periodic Motion

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 chair of mass 30 kg on top of a spring oscillates with a period of 2s. (a) Find the spring's force constant. You place an object on top of the chair, and it now oscillates with a period of 3s. (b) Find the object's mass.

(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?

(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?

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(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.] <IMAGE>

(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.

(II) A fisherman’s scale stretches 3.2 cm when a 2.4-kg fish hangs from it.

(b) 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?

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.

(a) What is the frequency of oscillation?

(II) A 0.350-kg mass oscillates on the end of a thin vertical spring (spring constant 265 N/m) with an amplitude of 28.0 cm. The mass passes through the equilibrium point (y = 0) with positive velocity at t = 0 .

(a) What equation describes this motion as a function of time?

A 62-kg person jumps from a window to a fire net 20.0 m directly below, which stretches the net 1.4 m. Assume that the net behaves like a simple spring.

(a) Calculate how much it would stretch if the same person were lying in it.

A particular unbalanced wheel of a car shakes when the car moves at 90.0 km/h. The wheel plus tire has mass 17.0 kg and diameter 0.58 m. By how much will the springs of this car compress when it is loaded with 280 kg? (Assume the 280 kg is split evenly among all four springs, which are identical.)

(I) (a) What is the equation describing the motion of a mass on the end of a spring which is stretched 7.8 cm from equilibrium and then released from rest, and whose period is 0.66 s?

(b) What will be its displacement after 1.8 s?

A 62-kg person jumps from a window to a fire net 20.0 m directly below, which stretches the net 1.4 m. Assume that the net behaves like a simple spring.

(b) How much would it stretch if the person jumped from 38 m?

(II) A 0.350-kg mass oscillates on the end of a thin vertical spring (spring constant 265 N/m) with an amplitude of 28.0 cm. The mass passes through the equilibrium point (y = 0) with positive velocity at t = 0 .

(b) At what times will the length of the spring be longest and shortest?

(II) 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.

(d) What will be its maximum acceleration, and where will it first be attained?

(II) A wood block of mass 52 g floats on a lake, bobbing up and down at a frequency of 3.5 Hz.

(b) 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.