# Simple Harmonic Motion Flashcards

What is the equation for the restoring force for simple harmonic motion?

F = -kx -kx = m × d^2x/dt^2 k = Constant for the material

What is an equation to find the acceleration during simple harmonic motion?

a = -ω^2x a = -Bω^2sin(ωt)

What is the equation to find velocity during simple harmonic motion?

v = Bωcos(ωt)

What are the equations to find the displacement during simple harmonic motion? (3)

x = Acos(ωt) x = Bsin(ωt) x = Ccos(ωt) + Dsin(ωt)

Describe the simple harmonic motion of a mass on a spring

-kx = m × d^2x/dt^2

==>

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

ω = √(k/m) [DO NOT LEARN THIS EQUATION]

Describe the simple harmonic motion of a capacitor and an inductor

Vc + VL = 0 q/c + LdI/dt = 0 q/c = -L(dq/dt)/dt q/c = -L(d^2q/dt^2) d^2q/dt^2 = -q/Lc ω = 1 / √ Lc [DO NOT LEARN THIS EQUATION]

What happens to an atom with ‘Z’ number of electrons with a centre of mass ‘c’ when an electric field is applied to it?

The centre of mass of the electrons (‘c’) moves by a distance of x from the origin position

What is the equation for the force on the electrons around an atom when an electric field is applied to it?

F = QE = ZeE

What is the equation for the restoring force on electrons around an atom when an electric field is applied?

F = -βx β = Constant for restoring force

What is the equation when the restoring force is in equilibrium force with the force of the electric field?

ZeE = -βx

You need to know what happens to the dipole moment when an electric field is on an atom. The equation folows:

p = Zex = Ze ( ZeE / β ) = (( Z^2 e^2 ) / β ) E

[YOU DO NOT NEAD TO LEARN THIS]

What happens when an electric field applied to an atom is suddenly removed? What are the equations for this?

Only the restoring force is present > F = Ma > Mass Electrons = ZMe > -βx = ZMe > ω = √ ( β / ( ZMe )) [DO NOT LEARN THIS]

How is the polarizibility calculated from the SHM of the atom when an electric field is removed?

a = -(x0)ω^2sin(ωt) = d^2x/dt^2

Where x0 = initial displacement

-βx = M(d^2x/dt^2) => -βx/M = d^2x/dt^2

-(x0)ω^2sin(ωt) = -βx/M

Describe SHM with a mass on a spring with a resistive force

Resistive force = -βv = -β × dx/dt

Restoring force: -kx - = m × d^2x/dt^2

Combining them: -kx -β(dx/dt) = m(d^2x/dt^2)

Describe SHM for a capacitor and inductor and a resistor

Capacitor Voltage: V = q/c Inductance Voltage: V = L(dI/dt) Resistor Voltage: V = IR L(dI/dt) + IR + q/c = 0 L(d^2q/dt^2) + (dq/dt)R + q/c = 0