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Note: 6 = /k/m is nature frequency of free vibration and stiffness of spring, k = 0.2N/mm and m = 0.5kg Question 2 (30 marks) A storage company needs to build storages which is designed as the cylinder with the doom (assume the doom is hemisphere) added in the top (Figure 2). As a design engineer, you are required to optimise the designs by using the minimum materials which means that you need to design the storages with minimum surface area for a given certain volume. Assume negligible width for the walls of the storage. Task a) Provide the equations that link the minimum surface area MSA with Volume, V and radius, R. for the storage (Assume the cylindrical storages have a flat bottom and hemispheric top) (8) b) Calculate the diameter of the storage that gives minimum surface for the storage given three volumes. V = 5m", V2 = 6 m' and V=8 m. (12) c) Plot the graph of surface area, with radius, R, when volume is equal to 5m (10) R RI L Figure 2 Question 2

Figure 3 shows the electric RC circuits, where Ris Resistance, Cis the capacity and represents Voltage and i represents the electric current. According to Kirchhoff's law, the relationship between the voltage, resistance, capacity and electric current can be written as: di R + = dt Task a) Using integration method demonstrate the electric current for RC circuit can be written as (i = at t=0) (13) V ie-/RC b) Find the electric current, i, when t=0.01s, t=0.1s, t=1s and t=5s if R=42 and C = 0.015F and voltage from a battery V = 80 V. (12) t=0 + VS. 70 W - Vc + 카 с Figure 3 Question 3 At Pass threshold The minimal requirements for this course work are that correctly using first and second order of differentiation to solve the engineering problems and by using differentiation to optimise the function and using integration methods to solve the engineering problems.