APPC Unit 8 SHM Simple Harmonic Motion Simple

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APPC Unit 8: SHM

APPC Unit 8: SHM

Simple Harmonic Motion Simple harmonic motion (SHM) refers to a certain kind of oscillatory,

Simple Harmonic Motion Simple harmonic motion (SHM) refers to a certain kind of oscillatory, or wave-like motion a pendulum a bob attached to a spring low amplitude waves in air (sound), water, the ground the electromagnetic field of laser light vibration of a plucked guitar string the electric current of most AC power supplies

Restoring Force The restoring force always acts in the opposite direction from the displacement

Restoring Force The restoring force always acts in the opposite direction from the displacement F is proportional to -x

Simple Harmonic Motion Equilibrium: the position at which no net force acts on the

Simple Harmonic Motion Equilibrium: the position at which no net force acts on the particle. Displacement: The distance of the particle from its equilibrium position. Usually denoted as x(t) with x=0 as the equilibrium position. Amplitude: the maximum value of the displacement with out regard to sign. Denoted as xmax or A.

The period and frequency of a wave Period (T) of a wave is the

The period and frequency of a wave Period (T) of a wave is the amount of time it takes to go through 1 cycle Frequency (f) is the number of cycles per time frequency and period are related as follows: Since a cycle is 2 p radians, the relationship between frequency and angular frequency is:

Position as a function of time

Position as a function of time

Calculus!

Calculus!

Let’s talk about Energy! Potential Kinetic energy is greatest at the amplitudes energy is

Let’s talk about Energy! Potential Kinetic energy is greatest at the amplitudes energy is greatest at equilibrium

Conservation of Energy Because SHM is all about restorative forces we can always apply

Conservation of Energy Because SHM is all about restorative forces we can always apply Conservation of Energy

The Simple Pendulum Object in SHM treated like a point mass Restoring force is

The Simple Pendulum Object in SHM treated like a point mass Restoring force is the x component of the force of gravity

The Simple Pendulum vs The Physical Pendulum

The Simple Pendulum vs The Physical Pendulum

The Physical Pendulum Now suppose that the mass is not all concentrated in the

The Physical Pendulum Now suppose that the mass is not all concentrated in the bob? In this case the equations are exactly the same, but the restoring force acts through the center of mass of the body (C in the diagram) which is a distance h from the pivot point

Period of a Physical Pendulum Here is the equation:

Period of a Physical Pendulum Here is the equation:

Torsion Pendulum

Torsion Pendulum

Torsion Pendulum If the disk is rotated through an angle (in either direction) of

Torsion Pendulum If the disk is rotated through an angle (in either direction) of θ, the restoring torque is given by the equation: