This behaviour can be reduced to an expression for the displacement as a function of time....

  

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This behaviour can be reduced to an expression for the displacement as a function of time. y(t) = et cos (2n ft) where k=0.58 and f = 2 Hz. a. Calculate the values of t in the interval t=0 s to t= 1 s for which the value of y(t) is zero. Hint: consider values at which a cosine function is zero and consider if there are any values at which the exponential function can be zero. b. Differentiate f(t) = et and g(t) = cos(27 ft) with respect to t. c. Differentiate the function y(t) to show that the expression for the velocity of the tip as a function of time can be written as: v (t) = -e [k cos(2xft) + 2nf sin(2xft)] d. Calculate the value off after the start at which the velocity of the tip first becomes zero? Hint. the expression for velocity is given in part (c) and remember to consider again if the exponential function can be zero. e. Find an expression for the acceleration of the tip. Time (s) 190 NO Displacement (mm) This behaviour can be reduced to an expression for the displacement as a function of time. y(t) = et cos (2n ft) where k=0.58 and f = 2 Hz. a. Calculate the values of t in the interval t=0 s to t= 1 s for which the value of y(t) is zero. Hint: consider values at which a cosine function is zero and consider if there are any values at which the exponential function can be zero. b. Differentiate f(t) = et and g(t) = cos(27 ft) with respect to t. c. Differentiate the function y(t) to show that the expression for the velocity of the tip as a function of time can be written as: v (t) = -e [k cos(2xft) + 2nf sin(2xft)] d. Calculate the value off after the start at which the velocity of the tip first becomes zero? Hint. the expression for velocity is given in part (c) and remember to consider again if the exponential function can be zero. e. Find an expression for the acceleration of the tip. Time (s) 190 NO Displacement (mm)