5.3 - Oscillations

Considering a spring oscillating - define displacement, amplitude, frequency, period.

Displacement - Distance from equilibrium position

Amplitude - Maximum displacement

Frequency - Number of oscillations per second

Period - Time taken for a complete oscillation

What are the conditions for SHM?

Acceleration must be directly proportional to displacement and in the opposite direction

It must act towards equilibrium

What is x as a function of t and ⍵

x = Acos⍵t or x = Asin⍵t

(where A is amplitude)

True or false: velocity is a maximum when displacement is a maximum

False.

The velocity is minimum at the amplitude of oscillation, as the object changes direction.

Velocity is maximum when object passes equilibrium position.

How can you calculate maximum velocity?

Vmax = ⍵A

For velocity, V = ±⍵√A² - x². Can be negative depending on direction.

What is damping?

Amplitude of oscillations decrease over time. This is due to energy lost to resistive forces such as drag or friction.

What is light damping, heavy damping and critical damping

Light damping occurs naturally - amplitude decreases exponentially

Heavy damping - Amplitude decreases dramatically. (e.g in water)

Critical damping - Object stopped in as short time as possible without overshooting equilibrium

What is the difference between free and forced oscillations?

Free oscillation - when an object oscillates without any external forces being applied, it oscillates at it’s natural frequency.

Forced oscillation - occurs when a periodic driving force is applied to an object which causes it to oscillate at a particular frequency.

What is resonance?

When driving frequency of an external force applied to an object is the same as the natural frequency of the object, resonance occurs.

This is when the amplitude of oscillation rapidly increases, and if there is no damping, the amplitude will continue to increase until the system fails.

Describe an experiment technique to investigate the resonance of an object?

Suspend a mass between 2 rings attached to an oscillation generator and use a ruler parallel with the spring-mass system to record amplitude.

Increase frequency of the generator slowly so that the amplitude increases, reaching maximum amplitude when the driver frequency is the same as the natural frequency of the system

Since drag force due to the air damps the system, the amplitude should not continue to increase until the point of system failure.

Increase accuracy - system can be filmed and amplitude recorded from video stills, as it can be difficult when mass is oscillating

Define SHM?

a = -⍵²x

Acceleration of an object is directly proportional to it’s displacement.

The negative sign mean acceleration of the object acts in direct opposite to the displacement (returns to equilibrium)