Question

Problem two: Cari won.no Track A frictionless cart of mass M is attached to a spring with spring constant k. When the cart is displaced 6 centimeters from its rest Rest position position and released, il oscillates with a period of 2 seconds. Four students are discussing what would happen to the period of oscillation if the original cart with mass M was displaced 12 cm o O from its rest position instead of 6 cm and again released: Ava: "Since the spring is stretched more, the force will be greater, causing a greater acceleration and greater speeds overall. Since the curt is moving faster, the time will go down, probably to / second since the force is doubled." Barb: “The curt hus farther to go now, and so it's going to take longer to make a complete cycle. li's going to go farther on both sides of the rest position, so the round-trip is 48 cm instead of 24 cm. The period is going to double." Charles: “The cart has four times as much energy, and the conjugate variable for energy is time according to the Heisenberg uncertainty principle. The energy quadruples when the spring stretch is doubled, and so the time must be only one-quarter as much. The period will be one-half second." Dorothy: "Stretching the spring twice as far means that kis twice as big. And the period is 2 pi times the square root of the spring constant divided by the mass. Doubling the spring constant and leaving the mass alone is going to double what's inside the square root, and after we take the square root we get a period of 2 seconds times the square root of 2. or 1.414 seconds." Which, if any, of these students do you agree with? Charles Ava None of them Dorothy Please explain your reasoning. Barb

Answer 1

or, a M - کرا M 2、经 According to Hook's law restoring force F=kn = ma her, ka = Ma k x=w2a Im angular frequency so time period not dedends on amplitude displacement : So all of them are wrong. When displacement is 12 cm then greater path has to be Cover but some time velocity increases such a way that both compensate and time period pemain Constant. None of them. 60 please give rating help me. Comment any doubt, sure help. Cs Scanned with CamScanner