A spring is mounted horizontally with its left end fixed. By connecting a spring balance to the free end and pulling to the right, we determine that the stretching force is proportional to the displacement and that a force of 6.0 N causes a displacement of 0.030 m. We remove the balance and connect a 0.50 kg slider to the end, pull it until it moves to x = 0.020 m through a frictionless air track, release it and see how it oscillates. Determine the slider position after 3.5 seconds.

Aplayground slide is 8.80 ft long and makes an angle of 25.0° with the horizontal. a 63.0-kg child, initially at the top, slides all the way down to the bottom of the slide. (a) choosing the bottom of the slide as the reference configuration, what is the system's potential energy when the child is at the top and at the bottom of the slide? what is the change in potential energy as the child slides from the top to the bottom of the slide? (include the sign of the value in your answer.)