Let’s say the graph above shows the acceleration as a function of time for a Tha

Question

Let’s say the graph above shows the acceleration 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 cm/s2. Note that the units on the time axis are milliseconds.

(a) Determine the angular frequency of the oscillations.

(b) Determine the amplitude of the oscillations. (Note that this is not the maximum value of the acceleration, which you can read off the graph above – we’re looking for the maximum magnitude of the turkey’s displacement from equilibrium.)

(c) Come up with an equation describing the x-position of the turkey as a function of time.

(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?

i.  x = -A

ii. x = -A/2

iii. x = 0

iv. x = +A/2

v. x = +A

(e) Sketch a graph of the x-velocity of the turkey as a function of time from t = 0 to t = 6 ms. What is the turkey’s maximum speed?

Explanation / Answer

1) 3

2) 8m

3)x=8cos(2t/6)=8cos(t/3)

4) v. +A

5)  would be a sin curve . curve at 0 would be 0 like after 4+1 unit

max value = v =dx/dt max =8sin(t/3)/3 max=8/3 as sin max = 1

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