Question

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1. A mass is attached to a horizontal spring, and oscillates with a period of 1.2 s and with an amplitude o 12 c Att-0s, the mass is 6 em to the left of the equilibrium position, and moving to the right a) On the plot of the cosine function below, label the two points that could correspond to the phase offset if you consider just the initial psition of the oscillator. What are the two possible values for the phase ofiet (measured in radians) phase (rad) Figure 1: A plot of cost) for part a) of this problem. b) What is the correct phase offset for this oscillator? Make sure you justify your answer c) Write down an expression for the position, velocity, and acceleration of the mass as a function of time. The only variable you should have in your expressions is time You can write your solution on the back of this page, or on a separate page. If you use a separate page, please staple this sheet to the front on your solo

Answer 1

Given data, Time period = 1.25 A = 12 cm a) The equation of this motion x = A Cos (w t + phi) Amplitude (A) = 12 cm we know that, given period T = 2 phi/w Therefore w = 2phi/t Therefore w = 2 phi/1.2 w = 1.67 phi Therefore But, time t = 0, x = -6 cm because it is to the left x = A cos (e t + phi) - 6 = 12 cos (1.67 phi times 0 + phi) phi = 2.094 rad [1 rad = 0.67 phi = 2/3 phi] phi = 4 phi/3 Therefore Two values of phase offset phi = 2 phi/3, 4 phi/3. B) The correct phase of the oscillator phi = 2 phi/3 c) x = A cos (w t + phi)