Question

An object of mass m=80 kg moves in one dimension subject to the potential energy

U(x)=λ4(x2−a2)2+b2x2.(1)

Here we use λ= 9 kg/(m2s2), a= 9 m, and b= 719 kg/s2.

(a) How many equilibrium points (stable and unstable ones) does this potential have?

n=
1
2
3
4
5?


(b) Find a stable equilibrium point x0 such that x0 is positive. (in meters)

x0=


(c) Do a Taylor expansion of the force F(x) for x close to the equilibrium point, x≃x0, that is F(x)=F0−k(x−x0)+… What are the values for F0 (in Newton) and k (in kg/s2)?

hint: For help on using Taylor series to express the potential energy function near a stable minimum, we encourage you to look at the following page in the section on small oscillations:here

F0=

k=

(d) What is the period T of small oscillations (in seconds) of this mass around the equilibrium point x0? (Note that the parameter k found in the previous question acts like a spring constant that wants to pull small deviations back to the equilibrium point)

T=

Answer 1

part (a) n=3

Answer 2

What about the remaining parts??

Answer 3

try x_0 = 3.75. i used alphawolfram to plot the graph

Answer 4

Are you kidding me? I'm in that MIT online class too, and you copied the TEST problem word for word! Did you even bother to read the honor code?!

Answer 5

You should be banned.

Answer 6

yep it is as bad from you as from them to insert taylor series out of the blue... let alone the rest...

Answer 7

@Anonymous - how did you came to the topic if you have not googled it? You are also a chater!