A system consisting of a block and a horizontally-mounted spring oscillates with simple harmonic motion. The position of the block relative to its equilibrium varies according to the following equation:

x(t)= 2Sin(π/2t+ π/4)

At what time (in s) after t = 0 s is the potential energy of the system first at a maximum?

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.