1. A particle of mass m moves in one-dimensional potential given by
V(x) = Am cos(x)
where λ, A > 0, with initial position xo and initial velocity vo. Draw a graph of the potential, and describe
the motion of the particle in the following cases:
TT
a) x₁ = and v₁ = 0;
22
b)
=
= 0 and v0 = 0;
3πt
22
Xo
c) Xo =
-
and vo= -2√A.
-
2. A particle is dropped in the presence of Stokes drag Farag = -bv, where is the velocity of the particle and
b> 0 is a constant. Write down the equation of motion in terms of , and show that the vertical component
of the equation of motion is satisfied by:
v₂(t) =
mg
19 (exp(-)-1)
b
What is the terminal velocity of the particle? Is it possible to determine the terminal velocity without solving
the equation of motion?
