17. Periodic Motion

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 position as a function of time.

In a physics lab, you attach a 0.200-kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s. Find the spring's force constant.

An oxygen atom at a particular site within a DNA molecule can be made to execute simple harmonic motion when illuminated by infrared light. The oxygen atom is bound with a spring-like chemical bond to a phosphorus atom, which is rigidly attached to the DNA backbone. The oscillation of the oxygen atom occurs with frequency ƒ = 3.7 x 10¹³ Hz. If the oxygen atom at this site is chemically replaced with a sulfur atom, the spring constant of the bond is unchanged (sulfur is just below oxygen in the Periodic Table). Predict the frequency after the sulfur substitution.

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?

The displacement of an oscillating object as a function of time is shown in Fig. E14.4. What is (c) the period? (d) the angular frequency of this motion?

A block attached to a spring with unknown spring constant oscillates with a period of 2.0 s. What is the period if the amplitude is doubled?

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?

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 100 g block attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless table. Its velocity is 20 c/m when 𝓍 = -5.0 cm What is the block's position when the acceleration is maximum?

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.

A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7 shows a graph of the ball's position x as a function of time t. What are the oscillation's (a) period, (b) frequency, (c) angular frequency, and (d) amplitude? (e) What is the force constant of the spring?

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?

(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.

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.