Unit 6: Simple Harmonic Motion

Simple Harmonic Motion (SHM)

Type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and is directed towards it.

Displacement

The distance of an object from its equilibrium position in Simple Harmonic Motion, given by x = A cos(ωt + φ).

Velocity

The rate of change of displacement in Simple Harmonic Motion, given by v = -Aω sin(ωt + φ).

Acceleration

The rate of change of velocity in Simple Harmonic Motion, given by a = -Aω^2 cos(ωt + φ).

Energy in SHM

The total mechanical energy of a system undergoing SHM is constant and is the sum of kinetic and potential energy.

Force in Simple Harmonic Motion

The force exerted by a spring in Simple Harmonic Motion, given by F = -kx, where k is the spring constant and x is the displacement.

Amplitude

The maximum displacement of a particle from its equilibrium position in a wave.

Period

The time it takes for one complete cycle of a wave to occur, denoted by T and measured in seconds (s).

Frequency

The number of complete cycles of a wave that occur in one second, denoted by f and measured in Hertz (Hz).

Formula for Period of a Pendulum

T=2π√(L/g)

Formula for Period of a Spring

T=2π√(m/k)

Formula for Total Energy in Simple Harmonic Motion

E = ½kA²

Formula for Kinetic Energy in Simple Harmonic Motion

K = ½mv²

Formula for Potential Energy in Simple Harmonic Motion

U = ½kx²

Where is velocity is maximum?

At the equilibrium position.

Where is velocity is minimum?

At the extreme positions.

What is the shape of a graph of simple harmonic motion relative to time?

Sinusoidal curve.

What is the spring constant?

Denoted as “k”. It tells us how strong the spring is, with a greater k being a stiffer spring.

How are frequency and period related?

Inversely related. For example, T = 1/f.

What can amplitude demonstrate about an object with simple harmonic motion?

The intensity and energy level of the object.