17. Periodic Motion

A mass oscillates on a vertical spring in simple harmonic motion. Which of the following best describes the graph of its $K$ (kinetic energy) as a function of $t$ (time)?

(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 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. What is the book's 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.

A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.0 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. What is the frequency of oscillation?

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. How much would it stretch if the person jumped from 38 m?

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.)

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 distance from equilibrium when the speed is 50 cm/s?

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. What equation describes this motion as a function of time?

Your lab instructor has asked you to measure a spring constant using a dynamic method—letting it oscillate—rather than a static method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses on the lower end, and start them oscillating. One of you uses a meter stick to measure the amplitude, the other uses a stopwatch to time 10 oscillations. Your data are as follows: Use the best-fit line of an appropriate graph to determine the spring constant.

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. At what times will the length of the spring be longest and shortest?

A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height 3.0 cm above the top of the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation frequency?

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