TOPIC 4.1 Kinematics of Simple Harmonic Motion

Oscillations Name some examples of oscillations How do you know they are oscillations?

Summary of some Oscillations Nature of oscillating system Potential Energy stored as Kinetic Energy possessed by moving Mass on helical spring Elastic energy of spring Mass Cantilever Elastic energy of bent ruler Ruler Simple pendulum Gravitational P.E. of bob Bob Mass floating in liquid of zero viscosity Gravitational P.E. of Mass Mass

Motion of a Simple Harmonic Oscillator What would each of the following look like? d-t graph v-t graph a-t graph

Simple Harmonic Motion is a WAVE!

Simple Harmonic Motion is periodic motion in which the restoring force is proportional and in the opposite direction to the displacement Consider the pendulum: What condition must be true for it to be considered a “simple harmonic oscillator”?

Do pendulums follow SHM?

Defining SHM “(Restoring)force is proportional to the displacement and in the opposite direction” a -x How did we go from force to acceleration?

Review Displayed below is a position-time graph of a mass on a spring Find the: Amplitude Period FrequencyAngular frequency 10 cm 0.2 s 5.0 Hz 10  rads -1

Angular Frequency What is one cycle here in radians? 22 What’s the definition of frequency?

Phase shift/difference is the time difference or phase angle by which one wave/oscillation leads or lags another.

Phase shift/difference, Φ

Great Website on… Oscillations How is SHM related to circular motion?

Velocity of SHM Watch the oscillating duck. Let's consider velocity now Remember that velocity is a vector, and so has both negative and positive values. Where does the magnitude of v(t) have a maximum value? Where does v(t) = 0?

Velocity of SHM Watch the oscillating duck. Let's consider velocity now Remember that velocity is a vector, and so has both negative and positive values. Where does the magnitude of v(t) have a maximum value? Where does v(t) = 0? C A and E

Acceleration of SHM Watch the oscillating duck. Let's consider acceleration now Remember that acceleration is a vector, and so has both negative and positive values. Where does the magnitude of a(t) have a maximum value? Where does a(t) = 0?

Acceleration of SHM Watch the oscillating duck. Let's consider acceleration now Remember that acceleration is a vector, and so has both negative and positive values. Where does the magnitude of a(t) have a maximum value? Where does a(t) = 0? A and E C

Summary 1 What are some parameters that are used to describe SHM? 1.amplitude (A) 2.period (T) 3.frequency (f) 4.angular frequency (  ) 5.initial phase (  ) 6.maximum velocity (v(t)max) and 7.maximum acceleration (a(t)max)

Summary 2 What is the minimum set of parameters to completely describe simple harmonic motion? 1.amplitude (A) 2.angular frequency (  ) 3.initial phase (  )

From the syllabus Define simple harmonic motion (SHM) and state the defining equation as a α -x a = acceleration x = displacement What is the significance of the negative sign?