Chapter 9: Periodic Motion, Waves, and Sound Flashcards
Simple Harmonic Motion is:
Repetitive motion of an oscillating system in which a particle or mass oscillates about an equilibrium position and is subject to a linear restoring force.
Equation to determine the restoring force of a spring (Hooke’s Law):
F = -kx
where k is the spring constant and x is the displacement of the spring from its equilibrium length
The higher the k value of a spring, the more:
stiff the spring is, and the greater the magnitude of restoring force for any given displacement
Equation to determine the acceleration of a spring:
a = -ω2x
where ω is the angular frequency and is equal to 2πf and rad(k/m)
Equation to determine the angular frequency (ω) of a spring:
ω = 2πf = √(k/m)
where m is the mass of the object
Frequency is a measure of:
the rate at which cycles of oscillation are being completed.
SI unit of frequency:
hertz (Hz)
SI unit of anglular frequency:
r/s (radians per second)
One radian is equal to:
180/π
so 2π radians is equal to 360 degrees (a full circle)
Two springs with identical k and m values but that are stretched at different lengths will always experience the same:
frequency of oscillation
Frequency describes:
the number of oscillations per second
A period describes:
how many seconds it takes for one oscillation to occur
A period is equal to:
1/f
where f is the frequency
Equation to determine the potential energy of a spring:
PE = 1/2kx2
Equation to determine the kinetic energy of a spring:
KE = 1/2mv2
A spring’s maximum velocity is at:
the equilibrium point (as it passes through it)
Equation to determine the restoring force of a pendulum:
F = -mgsinØ
where Ø is the angle between the pendulum arm and the vertical
Equation to determine the angular frequency (ω) of a pendulum:
ω = 2πf = √(g/L)
where L is the length of the pendulum
The two factors that contribute to the angular frequency of a spring:
the spring constant and the mass of the object
The two factors that contribute to the angular frequency of a pendulum:
gravity and the length of the pendulum
Equation to determine the potential energy of a pendulum:
PE = mgh
Equation to determine the kinetic energy of a pendulum:
KE = 1/2mv2
Equation to determine the period (T) of a spring:
T= 2π√(m/k)
Equation to determine the period (T) of a pendulum:
T = 2π√(L/g)
