Vibrations & Waves

In the example of a mass on a horizontal spring, m has a value of 0.80 kg and the spring constant, k, is 180 N/m. At time t = 0 the mass is observed to be 0.04 m further from the wall than the equilibrium position and is moving away from the wall with a velocity of 0.50 m/s. Obtain an expression for the displacement of the mass in the form x(t) = A cos(ωt+ϕ), obtaining numerical values for A, ω, and ϕ.

CH 1, Worked Example

A mass of 1.5 kg rests on a horizontal table and is attached to one end of a spring of spring constant 150 N/m. The mass on the spring is subjected to harmonic force of the form F(t) = F0cos(ωt) where F0 = 0.75 N and ω = 6π s-1. The damping constant b = 3.0 Ns/m. 1. Determine the amplitude and relative phase of the

steady state oscillations of the mass. 2. Show that if the applied frequency were adjusted

for resonance, the mass would oscillate with an amplitude of approximately 2.5 x 10-2 m.

CH 3, Worked Example