Aspring has a 12 cm length. when a 200-g mass is hung from the spring, it extends to 27 cm. the hanging mass were pulled downward a further 5 cm. what is the time-dependent function of the position, in centimeters, of the mass, assuming that the phase angle latex: \phi=0ϕ=0?

latex: x(t)=15\cos{(8.08\textrm{ }t)}x(t)=15cos⁡(8.08 t), where the coefficient inside the trigonometric function has units of rad/s.

latex: x(t)=5\cos{(8.08\textrm{ }t)}x(t)=5cos⁡(8.08 t), where the coefficient inside the trigonometric function has units of rad/s.

latex: x(t)=5\cos{(1.29\textrm{ }t)}x(t)=5cos⁡(1.29 t)x(t)=5cos⁡(1.29 t), where the coefficient inside the trigonometric function has units of rad/s.

latex: x(t)=15\cos{(1.29\textrm{ }t)}x(t)=15cos⁡(1.29 t)x(t)=15cos⁡(1.29 t), where the coefficient inside the trigonometric function has units of rad/s.

There is a theory that indicates that dinosaurs became extinct when about 65 million years ago, a large asteroid hit the earth surface. dust caused by this collision blocked the sunlight reaching the earth's surface and many forms of life became extinct due to the cold. fearing this threat, how large the radius of an asteroid should you be looking for if the dangerous asteroid size is approximately the same as the one that killed the dinosaurs? available data suggests that about 18% of that asteroid's mass ended up as a dust spread evenly over earth after eventually settling out of the upper atmosphere. about 0.0180 g/cm^2 of dust, which is chemically different than the earth's rock, covered the earth's surface. typical asteroids have a density of about 1.9 g/cm^3. now that we know the size of the asteroid, how much energy was released during impact, assuming all of it was just the kinetic energy of the asteroid right before the impact?

Use the information presented in the graph to answer the questions. which segments show acceleration? which segment indicates that the object is slowing down? what is the velocity of segment b? what is the acceleration of segment b?

Immediately upon reaching its lowest point, a falling pendulum bob has its greatest amount of energy, which is the initial amount of potential energy. a. heat; less than b. heat; more than c. kinetic; less than d. kinetic; more than