Energy in the SHO If the mass is at the limits of its mo-on, the energy is all poten-al. If the mass is at the equilibrium point, the energy is all kine-c. Again there is only poten-al energy at the turning points: When the mass is in between the turning point and the equilibrium: 16 Energy in the SHO The total energy is constant! Poten-al energy func-on of a spring: 17 Lecture Exercise A 4 kg block on a fric-onless table is aCached to a horizontal spring with k=400 N/m. The spring is ini-ally compressed with 5 cm. -5cm a) Find the work done on the block by the spring as the block moves from x= x1 = -5 cm to its equilibrium posi-on x2 = 0 cm b) Determine the func-on x(t) of the block c) Determine the func-on v(t) of the block e) Determine the accelera-on a(t) of the block 18 Lecture Exercise Solution A 4 kg block on a fric-onless table is aCached to a horizontal spring with k=400 N/m. The spring is ini-ally compressed with 5 cm. a) Find the work done on the block by the spring as the block moves from x= x1 = -5 cm to its equilibrium posi-on x2 = 0 cm 19 Lecture Exercise Solution A 4 kg block on a fric-onless table is aCached to a horizontal spring with k=400 N/ m. The spring is ini-ally compressed with 5 cm. b) Determine the speed v(t) of the block at x2 20 Lecture Exercise A 4 kg block on a fric-onless table is aCached to a horizontal spring with k=400 N/m. The spring is ini-ally compressed with 5 cm. c) Determine the func-on x(t) of the block 21 Lecture Exercise A 4 kg block on a fric-onless table is aCached to a horizontal spring with k=400 N/m. The spring is ini-ally compressed with 5 cm. c) Determine the func-on v(t) of the block 22 Lecture Exercise A 4 kg block on a fric-onless table is aCached to a horizontal spring with k=400 N/m. The spring is ini-ally compressed with 5 cm. d) Determine the func-on a(t) of the block 23