19 Oscillations - SHM, Damping, and Forcing

Practice flashcards for SHM concepts: defining equations, energy, phase, pendulums, damped and forced oscillations, and the link between SHM and circular motion.

The acceleration in SHM is directly proportional to the displacement x and directed toward the fixed point, so a = -w² x

-ω^2

The restoring force in SHM is F = _ x.

-k

At the equilibrium position in SHM, the acceleration is _.

0

At the equilibrium position in SHM, the resultant force is _.

0

The total energy E in SHM is constant and equals E = _.

1/2 m ω^2 A^2

The displacement in SHM is x = _(ωt + φ).

A sin

The velocity in SHM is v = _.

ω A cos(ωt + φ)

The acceleration in SHM is a = _ x.

-ω^2

The phase constant ∅ depends on the initial condition and gives the value of x when t = _.

0

If at t = 0, x = +A, the phase ∅ equals _.

π/2

At x = ±A, the velocity v = _.

0

The potential energy in SHM is U = _.

1/2 m ω^2 x^2

The kinetic energy in SHM is K = _.

1/2 m v^2

Total energy E in SHM is E = _.

1/2 m ω^2 A^2

For SHM, F = - dU/dx implies F = _ x.

• m ω^2

In the SHM–Uniform Circular Motion relation, the angle is θ = _ t.

ω

For a simple pendulum (small angle), ω^2 = _.

g/L

For a mass-spring system, ω^2 = _.

k/m

The period of a mass-spring system is T = _.

2π sqrt(m/k)

The horizontal spring-mass oscillator period is independent of the force of gravity, i.e., T is independent of _.

gravity

Damped oscillations cause amplitude to _ with time.

decrease

Underdamped: the system still _.

oscillates

Critical damping returns to equilibrium in the shortest time without .

oscillation

Overdamping returns to equilibrium with a very long time to return without undergoing any .

oscillation

In free oscillations with no damping, the amplitude is .

constant

In forced oscillations, the frequency of the driven oscillation equals the frequency of the .

driving force

Resonance occurs when the driving frequency equals the natural frequency, causing the amplitude to .

increase dramatically

The maximum speed in SHM is vmax = .

ω A

The maximum acceleration in SHM is amax = A.

ω^2

The angular frequency for a simple pendulum is ω = _ when considering small angles.

√(g/L)

The time-period for a simple pendulum at small angles is T = _.

2π sqrt(L/g)

For a mass–spring SHM, ω = _ and T = 2π sqrt(m/k).

√(k/m)

The period of a horizontal mass–spring oscillator is independent of the gravitational acceleration because gravity acts only in the vertical direction and does not affect the horizontal restoring force, so T is independent of _.

gravity

In the relationship between SHM and Uniform Circular Motion, θ = _ t.

ω t

In a damped oscillator with increasing damping, the resonance peak amplitude tends to and the resonant frequency shifts to a _ frequency.

decrease; lower