New Note

The restoring force of a mass on a spring is given by __________.

-kx

The equation of motion for a mass on a spring is __________.

d^(2)x/dt^(2) = -k/m * x

The solution for a mass on a spring is represented as __________.

x = A cos(ωt - φ)

The equation for torque on a bar suspended by a cable is __________.

-κθ = I * d^(2)θ/dt^(2)

The solution for the dynamic system of the bar is __________.

θ = A cos(ωt - φ)

The frequency of oscillation is related to the angular frequency by the formula __________.

ω = 2π/T

The complex number representation of oscillation combines __________ functions and __________ functions.

trigonometric; exponential

For a spring, κ can be determined from __________ or __________.

the given force; displacement

The condition for real solutions in the harmonic equation requires __________ and __________.

A = B star; B = A star

The solutions to the harmonic oscillator without friction are characterized by __________.

a simple harmonic oscillator with a cosine function.

In damped oscillations, when γ/2 < ω_0, the solution involves __________ exponentials.

complex

The function describing a damped oscillator with moderate friction can be expressed as __________.

x = Ce^(-γ/2t)cos(ω' t + φ)

To find A and B in oscillating systems, one must use __________ data.

initial position and velocity

The equation for a driven harmonic oscillator is __________.

x double dot + γ x dot + ω_0^2 x = F/m cos ωt

The impedance in a driven oscillator can be defined as __________.

I = ω_0^2 - ω^2 + iωγ