Question

Please help me with 6; this chapter deals with second order autonomous differential equations.

model with a "soft 6. The equation in Exercise 4 is a spring-mass spring has a restoring force proportional to x - x3, rather th portrait, describe as precisely as you can what happens to the mass if it starts at mas with velocity x 2.5. What happens if it starts at x 0 with velocity x'4 x. Using the phase

Answer 1

F=k(x-x3),where k is spring constant

On differentiating the equation given in 4. exercise ,we get

x`+3x

and F=mg where g is gravity

On equating both the equations

mg = k(x-x3)

putting x = x`+3x

we get mg = k(x`+3x-(x`+3x)3)

So by this equation mass increases at x` =2.5 while at x` = 4 mass reduces because at this x becomes negative.