17. Periodic Motion

A spring with spring constant $2500\text{ N/m}$ has one end connected to the ceiling and the other end fastened to a $3.0\mathrm{kg}$ mass. The mass is oscillating with amplitude 3.0 cm. How fast is the mass moving when it is $2.0\mathrm{cm}$ above the equilibrium position?

A $2.0\mathrm{kg}$ block is gently lowered onto a vertical spring, and the spring compresses $5.0\mathrm{cm}.$ Another block is added, and the spring compresses an additional $3.0\mathrm{cm}.$ What is the mass of the second block added?

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. b. What will be the car's oscillation frequency while carrying four 70 kg passengers?

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?

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 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 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. c. What is the book's 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. b. 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 b. Distance from equilibrium when the speed is 50 cm/s?

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?