Classical Mechanics: Intermediate Flashcards
Define specific gravity
What is Archimedes’ principle?
The upward bouyant force on a mass submerged in a fluid is equal to the weight of fluid displaced by the mass, i.e. the volume of the space occupied by the mass beneath the surface of the fluid times the density of the fluid.
What is the volumetric flow rate for a fluid?
What is Bernoulli’s equation, and when does it apply?
Bernoulli’s equation applies to incompressible, steady flow, very low (approximately zero) viscosity fluids only.
Condition for resonance
The period of the driving function f(t) is equal to the period of the corresponding homogenous solution to the ordinary differential equation
Definition of Lagrangian
Euler-Lagrange Equations
Momentum canonically conjugate to q
What condition is equivalent to the conservation of the momentum conjugate to q?
The Lagrangian does not depend on the coordinate q
Definition of Hamiltonian
Typical expression for Hamiltonian, and scope of validity.
The expression given is valid if and only if the potential does not depend explicitely on velocities or time, i.e. depends only on the (generalized) coordinates.
Hamilton’s equations of motion
Natural angular frequency of a spring
Resonant frequency for a (possibly damped) spring
Damping paramter of a spring
Amplitude proportionality of an undamped oscillator
Overdamping vs Underdamping
The situation is overdamped if the damping parameter exceeds the natural frequency. The other two cases follow trivially.
Virial theorem for potentials which are directly proportional to the nth power of the inter-particle distance
