When bobbing for apples a child noticed that apples that get away bob up and dow

Question

When bobbing for apples a child noticed that apples that get away bob up and down, just like a vertical spring osculating up and down. The child measures the time it takes for a particular apple to complete one whole cycle of bobbing, and found it to be 0.3 seconds. If this apple was initially displaced by 0.01 m, answer the following questions. a) What is the period of oscillation of the apples motion 0.3 seconds b) Whet is the frequency of oscillation of the apples motion 3.34 Hz c) What is the angular frequency of oscillation of the apples motion. 20.94 rad/s d) What is the amplitude of the oscillation? 0.01 m e) The water a acting like a spring. If the mass of the apple was 0.01 kg, what would the equivalent spring constant of the water be? 4.386 N/m f) What is the position of the ball after 5 seconds? -0.005 m g) What is that velocity of the bail after 5 seconds? 0.179 m/s h) What is the acceleration of the ball after 5 seconds? 2.276 m/s^2

Explanation / Answer

g) we have x = A sin wt

v = Aw cos wt

a = -Aw^2 sin wt

from part f, x = A sin wt = -0.005, hence sin wt= -0.5, so cos wt = 0.866

v = 0.01*0.866*2 pi/0.3

= 0.181 m/s

h) a = 0.005*[2pi/0.3]^2 = 2.19 m/s^2

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