Feynman Simplified 1B Cover

Guide to the Cosmos
Making the Wonders of our Universe

Accessible to Everyone

Robert L. Piccioni, Ph.D.

Feynman Lectures Simplified

Feynman Simplified
ebook series
Feynman Simplified
Feynman Simplified
print book series
Award winning books
Shop Now
About Dr. Piccioni
Free Videos
mailbox Newsletter SignUp

1B: Harmonic Oscillators
& Thermodynamics

Feynman Simplified 1B covers the 2nd quarter of the freshman course of The Feynman Lectures on Physics. The topics we explore include:
  • Harmonic Oscillators, Resonances, and Transients
  • Kinetic Theory of Gases
  • Statistical Mechanics
  • Thermodynamics


The simplest mechanical example of behavior governed by a linear differential equation is a mass on a spring, illustrated in Figure 12-1. Here m is the mass, x is the vertical height, and x = 0 is the equilibrium height, the height at which that mass can rest motionless on this spring.

Mass on a Spring

We’ll assume the spring is ideal, perfectly elastic and obeys Hooke’s law: it exerts a force F = –kx, where k is the spring constant. The minus sign signifies that the force opposes the displacement x: if we compress the spring by moving the mass to +x, the spring’s force is directed downward, and vice versa. The differential equation is then:

F = ma = –kx
d2x/dt2 = –(k/m) x

The figure below shows a collision between two different atoms as viewed in their center of mass (CM). The diagonal line is the axis of symmetry, which passes through the centers of both atoms and their point of contact. The symmetry axis is rotated from the incoming direction by the angle .

Call the masses of the two atoms m1 and m2. The atoms’ velocities are u1 and u2 before the collision and v1 and v2 afterward.

We will shortly show that the magnitude of each atom’s velocity, its speed, is the same before and after the collision. With that we see the v’s are at the same angles to the axis of symmetry as are the u’s. Thus the scattering angle of each atom is: θ=π–2.

for $7.99

Click on one
of the following

Feynman Lectures
Simplified 1B:

Barnes & Noble


See all the
books in the

ebook Series

Now available
in print format