17. Periodic Motion

Which of the following best describes simple harmonic oscillation for a mass attached to a horizontal spring?

Given that the displacement of an object attached to a horizontal spring is described by $x=Acos(\omega t+\phi )$, which of the following statements is correct about the motion of the object?

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?

(II) The graph of displacement vs. time for a small mass m at the end of a spring is shown in Fig. 14–30. At t = 0, 𝓍 = 0.43 cm. (a) If m = 7.7 g, find the spring constant, k. (b) Write the equation for displacement 𝓍 as a function of time.

It has recently become possible to 'weigh' DNA molecules by measuring the influence of their mass on a nano-oscillator. FIGURE P15.58 shows a thin rectangular cantilever etched out of silicon (density 2300 kg/m³) with a small gold dot (not visible) at the end. If pulled down and released, the end of the cantilever vibrates with SHM, moving up and down like a diving board after a jump. When bathed with DNA molecules whose ends have been modified to bind with gold, one or more molecules may attach to the gold dot. The addition of their mass causes a very slight—but measurable—decrease in the oscillation frequency. A vibrating cantilever of mass M can be modeled as a block of mass ⅓M attached to a spring. (The factor of ⅓ arises from the moment of inertia of a bar pivoted at one end.) Neither the mass nor the spring constant can be determined very accurately—perhaps to only two significant figures—but the oscillation frequency can be measured with very high precision simply by counting the oscillations. In one experiment, the cantilever was initially vibrating at exactly 12 MHz. Attachment of a DNA molecule caused the frequency to decrease by 50 Hz. What was the mass of the DNA?

Determine the phase constant ϕ in Eq. 14–4 if, at t = 0, the oscillating mass is at 𝓍 = ― A.

Determine the phase constant ϕ in Eq. 14–4 if, at t = 0, the oscillating mass is at 𝓍 = A .

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 v_x = -30 cm/s. Determine: The position at t = 0.40 s.