17. Periodic Motion

A mass swinging at the end of a pendulum has a speed of 1.32m/s at the bottom of its swing. At the top of its swing, it makes a 9° with the vertical. What is the length of the pendulum?

(II) A 0.735-kg block oscillates on the end of a spring whose spring constant is k = 41.0 N/m . The mass moves in a fluid which offers a resistive force F = ― bv, where b = 0.662 N • s/m .

(a) What is the period of the motion?

(II) A vertical spring of spring constant 115 N/m supports a mass of 58 g. The mass oscillates in a tube of liquid. If the mass is initially given an amplitude of 5.0 cm, the mass is observed to have an amplitude of 2.0 cm after 3.5 s. Estimate the damping constant b. Neglect buoyant forces.

(II) An 1150-kg automobile has springs with k = 14,000 N/m . One of the tires is not properly balanced; it has a little extra mass on one side compared to the other, causing the car to shake at certain speeds. If the tire radius is 42 cm, at what speed will the wheel shake most?

(III) The amplitude of a driven harmonic oscillator reaches a value of 23.7 F₀ / k at a resonant frequency of 418 Hz. What is the Q value of this system?