1. Sketch y(t)vs.t graph to describe the vertical motion of the buoy over time.

Question

1. Sketch y(t)vs.t graph to describe the vertical motion of the buoy over time. Clearly label the amplitude and period of oscillation of the buoy in the graph with numerical values. Assume the origin of the graph is at t=0 and y=0

2. Based on the graph in part 1, write down the funtion y(t) that describes the vertical motion of the buoy. Substitute in numerical values for all variables that can be determined.

3. What is the vertical velocity v of the buoy at time t=0.5seconds?

4. What is the horizontal velocity u of the traveling water waves?

5. Write down the function y(x,t) that describes the height of the water wave.

Question 2: A buoy floats on the surface of the sea as transverse water waves pass beneath it at speed u. The waves cause the buoy to move up and down in simple harmonic motion, with a period of T 4 seconds. The maximum and minimum height of the buoy differ by 1 meter. At time t 0, the buoy is passing through its equilibrium position at x 0 and v = 0 as shown in the diagram below. buoy 5m (a) (10 points) Sketch a y(t) vs. t graph below to describe the vertical motion of the buoy over time. Clearly label the amplitude and period of oscillation of the buoy in your graph with numerical

Explanation / Answer

1. y(t) vs t is the samne graph as shown in the figure. just change the labels on the x and y axis
2. y = Asin(wt)
now, A = 0.5 m
w = 2*pi*f = 2*pi/4 = 1.57 rad/s
so, y = 0.5sin(1.57*t)
3. v = Awcos(wt)
T = 0.5S
V = 0.555 m/s
4. u = wavelength*freq = 10*0.25 =2.5 m./s

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