2. The displacement of a mass is given by the function y = sin 3t. The tasks are to: a) Draw a graph of the displacement y(m) against time t(s) for the time t = 0s to t = 2.5. b) Identify the position of any turning points and whether they are maxima, minima or points of inflexion. c) Calculate the turning points of the function using differential calculus and show which are maxima, minima or points of inflexion by using the second derivative. Compare your results from parts b and c. 3. The equation for the instantaneous voltage across a discharging capacitor is given by v = Voe" 7, where Vo is the initial voltage and r is the time constant of the circuit. The tasks are to: a) Draw a graph of voltage against time for V. = 121 and r = 2s, between t = 0s and t = 10s. b) Calculate the gradient at t = 2s and t = 4s. c) Differentiate v = 12ez and calculate the value of # at t = 2s and t = 4s. d) Compare your answers for part b and part c. e) Calculate the second derivative of the instantaneous voltage (2=) 4. The same capacitor circuit is now charged up to 12V and the instantaneous voltage is v = 12 (1 - e-=). The tasks are to: a) Differentiate v with respect to t to give an equation for . b) Calculate the value of " at t = 2s and t = 4s. c) Find the second derivative () 5. The gain of an amplifier is found to be G = 20 log(10Vat), The tasks are to find equations for: d'G a) dG b) dV out dV Out