Problem 4 Damped Oscillator Consider the lightly damped harmonic oscillator. We found the solution (in one of the forms) to be: x(t) = Ae¯¾¹ cos (w₁t + 6). Let the phase angle be zero. (a) What is the initial position and velocity with this choice of phase angle? What does the velocity you found tell you about the shape of the position versus time plot near t=0? (b) Find an expression for ä(t). Find the values of that give you a positive, negative, and zero acceleration at t = 0. (c) Sketch the position versus time for the case when ä(t = 0) > 0 and the case when ä(t = 0) < 0.

Problem 4 Damped Oscillator Consider the lightly damped harmonic oscillator. We found the solution (in one of the forms) to be: x(t) = Ae¯¾¹ cos (w₁t + 6). Let the phase angle be zero. (a) What is the initial position and velocity with this choice of phase angle? What does the velocity you found tell you about the shape of the position versus time plot near t=0? (b) Find an expression for ä(t). Find the values of that give you a positive, negative, and zero acceleration at t = 0. (c) Sketch the position versus time for the case when ä(t = 0) > 0 and the case when ä(t = 0) < 0.