Blog of Andrés Aravena
CMB2:

# Exercises after Class 8

10 March 2017

The next week we will have a graded quiz. It will be like an exam and it will allow you to practice for the real exam.

To prepare for that, please take the code of the function simulate that we developed in classes, and put it in a .Rmd file. The code is:

simulate <- function(N, pos_init, speed_init, force, mass, delta) {
pos <- rep(NA, N)   # N: number of times we use the "flash"
speed <- rep(NA, N) # first position and first speed
pos[1] <- pos_init
speed[1] <- speed_init
for(step in 2:N){
accel <- force(pos[step-1], speed[step-1], mass)/mass
speed[step] <- speed[step-1] + delta * accel
pos[step] <- pos[step-1] + delta * speed[step]
if(pos[step] <= 0) { # if we hit the floor...
speed[step] <- -speed[step] # we bounce
}
}
return(pos)
}

In the same .Rmd file you should include these two functions:

gravity <- function(pos, speed, mass) {
force <- -9.8*mass # -g times mass
return(force)
}

coil <- function(pos, speed, mass, K=20, L=1) {
force <- K*(L-pos)
return(force)
}

And then add two graphics, like this:

plot(simulate(N=200, pos_init=1.5, speed_init=5, force=gravity, mass=1, delta=0.01))
plot(simulate(N=200, pos_init=1.5, speed_init=5, force=coil, mass=1, delta=0.01))

## Questions:

Find the R code to determine:

• What is the highest position reached by the ball in each one of the two simulations?
• What is the time of flight? That is, how many steps are required to hit the floor?
• How do these two values (highest position, time of flight) change when you change the initial speed to a value between -5 and 10?