PROBLEM 1-8 points et\'s say the graph shows the velocity as a function of time

Question

PROBLEM 1-8 points et's say the graph shows the velocity as a function of time for a Thanksgiving turkey experiencing simple harmonic motion (oscillating along a line parallel to the x axis), and the units on the vertical scale are in mm/s. Note that the units on the time axis are milliseconds 4 6 (ms) -4 -8 [1 point] (a) Determine the angular frequency (o, in rad/s) of the oscillations [2 points] (b) Determine the amplitude of the oscillations. (Note that this is not the maximum value of the velocity, which you can read off the graph above we're looking for the maximum magnitude of the turkey's displacement from equilibrium.) [2 points] (c) Come up with an equation describing the x-position of the turkey as a function of time [1 point] (d) If we define A as the amplitude of the oscillation, and define x - 0 as the turkey's equilibrium position, at what location on the x-axis is the turkey at t -0? [2 points] (c) Sketch a graph of the x-acceleration of the turkey as a function of time from t 0 to 6 ms. What is the turkey's maximum acceleration?

Explanation / Answer

Angular velocity is = Pi / 3Pi = 333.33 rad/s

From the figure we can see that half of the loop i.e. Pi radians cut the time axis at 1.5 Pi and 4.5 Pi.

We know that maximum velocity is given as multiplication of amplitude and frequency

8 * 2Pi/ 333.33 = A

d) x= 0

A = 18.84 mm

Equation will be

X = 18.84 sin (333.33*t)

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