Suppose an object of mass m is attached to the end of a spring hanging from the ceiling. The mass is at its equilibrium position y = 0 when the mass hangs at rest. Suppose you push the mass to a position yo units above its equilibrium position and release it. As the mass oscillates up and down (neglecting air friction), the position y of the mass after t seconds is given by the equation below. Use this equation to answer the questions below:

y = yocos (t square root k/m)

a) Find dy/dx, the velocity of the mass. Assumie k and m are constant.
b) How would the velocity be affected if the experiment were repeated with four times the mass on the end of the spring?
c) How would the velocity be affected if the experiment were repeated with a spring that has 4 times the stiffness (if k is increased by a factor of 4)?
d) Assume that y has units of meters, t has units of seconds, m has units of kg and k has units of kg/s2. Show that the units of the velocity in part a) are consistent.

Use the library or internet to research each planet. make a chart comparing the following: approximate surface temperature relative surface gravity compared to earth atmospheric gases water in any form: solid, gas, or liquid when you have completed your chart, use the information you have collected to answer the following questions: which is the hottest planet? which is the coldest planet? which planet's temperature is closest to that of earth? (note: water boils at 100°c/212°f. water freezes at 0°c/32°f) which planet has the greatest gravitational attraction? which planet has the least gravitational attraction? which planet's gravitational pull is closest to that of earth? do any of the planets have oxygen in their atmosphere? which planet's atmosphere most resembles that of earth? do any of the planets have flowing water? which planet's water resources (solid, gas, or liquid) might be close to the amount on earth? which planet most resembles earth in terms of all of the factors: temperature, gravity, atmosphere, and water? if earth became an uninhabitable planet, which planet do you think would be the next best to live on? explain your answer.