17. Periodic Motion

For a mass $m$ oscillating with amplitude $a$ at the end of a vertical spring with spring constant $k$, what is the period of the oscillation?

Four mass–spring systems oscillate in simple harmonic motion on a frictionless horizontal surface. Each system has a different mass and spring constant. Which system will have the greatest angular frequency of oscillation?$\omega =\sqrt{\frac{k}{m}}$

$$A mass attached to a horizontal spring oscillates on a frictionless surface. Which of the following statements is true about its motion?

A simple harmonic oscillator consists of a block of mass $m$ attached to a horizontal spring with force constant $k$. What is the period of oscillation of the block on a frictionless surface?

Which of the following is not an example of approximate simple harmonic motion?

Which one of the following statements is true concerning an object executing simple harmonic motion attached to a horizontal spring?

Which of the following equations correctly gives the position of a simple harmonic oscillator attached to a horizontal spring as a function of time?

A mass-spring system with an angular frequency ω = 8π rad/s oscillates back and forth. (a) Assuming it starts from rest, how much time passes before the mass has a speed of 0 again? (b) How many full cycles does the system complete in 60s?

A 4-kg mass on a spring is released 5 m away from equilibrium position and takes 1.5 s to reach its equilibrium position. (a) Find the spring's force constant. (b) Find the object's max speed.

What is the equation for the position of a mass moving on the end of a spring which is stretched 8.8cm from equilibrium and then released from rest, and whose period is 0.66s? What will be the object's position after 1.4s?

Carbon dioxide is a linear molecule. The carbon–oxygen bonds in this molecule act very much like springs. Figure 14–45 shows one possible way the oxygen atoms in this molecule can oscillate: the oxygen atoms oscillate symmetrically in and out, while the central carbon atom remains at rest. Hence each oxygen atom acts like a simple harmonic oscillator with a mass equal to the mass of an oxygen atom. It is observed that this oscillation occurs with a frequency of ƒ = 2.83 x 10¹³ Hz. What is the spring constant of the C-O bond?