Questions 6-8: In lab, you attach a 0.5 kg cart to a compressible spring with stiffness 30 N/m. With the +x axis defined to the right and x = 0 defined at the location where the spring is relaxed, you pull the cart to the right a small distance, to x0 = 0.28 m, and you release it from rest. (Define this as t = 0.) As a result, the cart oscillates without crashing into the end of the track. The frictional force on the cart by the track is very small. x=0 6. What is the x-position of the cart at t=0.284s? (a) 0.273 m (b) 0.26 m (c) 0.0865 m (d) -0.165 m (e) 0.28 m

A block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown in Figure P7.15. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is k = 0.350. Figure P7.15

Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.

A vibration sensor, used in testing a washing machine, consists of a cube of aluminum 1.50 cm on edge mounted on one end of a strip of spring steel (like a hacksaw blade) that lies in a vertical plane. The strips mass is small compared with that of the cube, but the strips length is large compared with the size of the cube. The other end of the strip is clamped to the frame of the washing machine that is not operating. A horizontal force of 1.43 N applied to the cube is required to hold it 2.75 cm away from its equilibrium position. If it is released, what is its frequency of vibration?