17. Periodic Motion

A 200 g air-track glider is attached to a spring. The glider is pushed in 10 cm and released. A student with a stopwatch finds that 10 oscillations take 12.0 s. What is the spring constant?

An air-track glider attached to a spring oscillates with a period of 1.5 s. At t = 0 s the glider is 5.00 cm left of the equilibrium position and moving to the right at 36.3 cm/s. What is the phase constant?

A 500 g wood block on a frictionless table is attached to a horizontal spring. A 50 g dart is shot into the face of the block opposite the spring, where it sticks. Afterward, the spring oscillates with a period of 1.5 s and an amplitude of 20 cm. How fast was the dart moving when it hit the block?

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t = 0 s. It then oscillates with a period of 2.0 s and a maximum speed of 40 cm/s. What is the glider's position at t = 0.25 s?

A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vₓ = -30 cm/s. Determine: The total energy.

(II) A small fly of mass 0.28 g is caught in a spider’s web. The web oscillates predominantly with a frequency of 4.0 Hz. At what frequency would you expect the web to oscillate if an insect of mass 0.46 g is trapped?

(II) A tuning fork oscillates at a frequency of 441 Hz and the tip of each prong moves 1.8 mm to either side of center. Calculate the maximum speed.

(II) A tuning fork oscillates at a frequency of 441 Hz and the tip of each prong moves 1.8 mm to either side of center. Calculate the maximum acceleration of the tip of a prong.

(II) A 0.25-kg mass at the end of a spring oscillates 3.2 times per second with an amplitude of 0.15 m. Determine the speed when it is 0.10 m from equilibrium.

At t = 0, an 885-g mass at rest on the end of a horizontal spring (k = 184 N/m) is struck by a hammer which gives it an initial speed of 2.12 m/s. Determine the period and frequency of the motion.

(II) At t = 0, an 885-g mass at rest on the end of a horizontal spring (k = 184 N/m) is struck by a hammer which gives it an initial speed of 2.12 m/s. Determine the amplitude.

A 0.25-kg mass at the end of a spring oscillates 3.2 times per second with an amplitude of 0.15 m. Determine the equation describing the motion of the mass, assuming that at t = 0, 𝓍 was a maximum.

A glider on an air track is connected by springs to either end of the track (Fig. 14–41). Both springs have the same spring constant, k, and the glider has mass M. Determine the frequency of the oscillation, assuming no damping, if k = 125 N/m and M = 215 g.

(III) A mass m is connected to two springs, with spring constants k₁ and k₂ in two different ways as shown in Fig. 14–33a and b. Show that the period for the configuration shown in part is given by $T=2\pi \sqrt{m(\frac{1}{k_1}+\frac{1}{k_2})}$. Ignore friction.

(III) A mass m is at rest on the end of a spring of spring constant k. At t = 0 it is given an impulse J by a hammer. Write the formula for the subsequent motion in terms of m, k, J, and t.