Question

(1A) A vertical spring with a spring constant of 8 N/m and damping constant of 0.05 kg/s has a 2 kg mass suspended from it. A harmonic driving force given by F = 2 cos(1.5 t ) is applied to the mass. What is the natural angular frequency of oscillation of the mass? What is the amplitude of the oscillations at steady state? Does this amplitude decrease with time due to the damping? Why or why not?

(1B) Two traveling waves with the same amplitude A, frequency f, and wavelength λ, but out of phase with each other by one quarter of a wavelength, are both traveling to the right and superpose in space. Find the amplitude, wavelength, and frequency of the resulting wave in terms of the given symbols. Write the equation of the resulting traveling wave y ( x , t ).

(1C) Standing waves are set up on a 1.5 m long string under tension and fixed at both ends. If the distance between nodes along the string is 0.25 m what is the wavelength of this mode and what harmonic is it?

Answer 1