A particle, of mass 9 kg, is attached to two identical springs. The other ends of the springs are attached to fixed points, A and B, which are 1.2 metres apart on a smooth horizontal surface. The springs have modulus of elasticity 45 N and natural length 0.4 m. The particle is released from rest at a distance of 0.5 metres from B and moves on the line AB. The midpoint of AB is C. At time t seconds after release, the displacement of the particle from C is x metres, where the direction from A to B is taken to be positive. www C wwww A B (a) Show that the resultant force on the particle, at time t, is -225x newtons. (b) Hence show that the particle moves with simple harmonic motion. (c) State the period of this motion. (d) Find the speed of the particle when it is 0.05 metres from C.

2. Thermal Efficiency a. Planet Express Generating Station in New York, NY uses 8720 Btu of energy to generate each kilowatt hour of electricity. Find its thermal efficiency. Express as a percentage with no decimal point. b. Mystery Shack Generating Station in Gravity Falls, OR has a thermal efficiency of 43%. How many million cubic feet (MMcf) of natural gas are needed to generate 560 megawatt hours of electricity? Round to the nearest hundredth.