Question Sheet 10 - Challenge Problem

1a) The equation of motion for a damped oscillator is x''(t)+(b/m)x'(t)+(k/m)x(t)=0. Set k = 5 N/m and m = 2 kg (remember to include the units in your code). Solve the differential equation.

b) Make a function, depending on b and t, with the output of the above DE as its RHS.

c) Now make a function which plots the above function over the range t from 0 to 10. (Remember to label your axes!)

d) Use manipulate to animate this plot for a range of values for b from 1 to 10.

e) The range of the x(t) axis changes depending on the value of b in our above manipulate, so it is not very useful for comparing the output for different values of b. Create a new function, which has a Plot[ ] function with a fixed range. Then make a manipulate of this function.