Find the probability density function f(x) for the position x of a particle which is executing simple harmonic motion on (-a, a) along the x axis. (see chapter 7, section 2, for a discussion of simple harmonic motion.) hint: the value of x at time t is x a cos wt. find the velocity da/dt; then the probability of finding the particle in a given dax is proportional to the time it spends there which is inversely proportional to its speed there. don't forget that the total probability of finding the particle somewhere must be 1

You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. the car goes up a 10-m highhill, then descends 15m to the track's lowest point. you'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. for safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top. a) what spring constant (k) should you specify ? b) what is the maximum speed of a 350 kg car if the spring iscompressed the full amount.