Oscillations

What is simple harmonic motion

Oscillating motion in which the acceleration of the object is given by:

a= -w^2 x

What are the key features of simple harmonic motion

a is proportional to x

The minus sign means that the acceleration of the object acts in the direction opposite to the displacement ( it returns the object to the equilibrium position)

Explain why the time period of an oscillator is independent of the amplitude

For example the period of a simple pendulum moving in SHM does not depend on the amplitude of the swing. As the amplitude increases so does the average speed of the spring, so the period does not change

Sketch a displacement time graph for an object in SHM

Define displacement in SHM

The distance from the equilibrium position

Define amplitude in SHM

The maximum displacement from the equilibrium position

Define time period in SHM

the time taken to complete one full oscillation

Define frequency in SHM

The number of complete oscillations per unit time

Explain the connection between circular motion and SHM

One complete oscillation has many of the same characteristics as one complete revolution in circular motion.

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Sketch a displacement time graph for an object moving with SHM

Sketch a velocity time graph for an object moving with SHM

Sketch an acceleration time graph for an object moving with SHM

State the two equations that can be used to describe how the displacement of a simple harmonic oscillator changes with time

x=Acoswt x=Asinwt

* If the object begins oscillating from its amplitude then at t=0 the object is at its positive amplitude so use the cosine version

* If the object begins oscillating from its equilibrium position then at t=0 the object is at it's equilibrium position and its displacement is 0 then use sine version

Which equation can be used to calculate the velocity of a simple harmonic oscillator at displacement x

How can the maximum velocity of a simple harmonic oscillator be determined

Vmax = wA

Explain why increasing angular frequency increases maximum velocity

The oscillator will be travelling the same distance in a shorter time interval. Therefore the maximum velocity Vmax of the oscillator ( when its displacement is x=0) will increase and this the gradient of the displacement time graph will increase

Explain why increasing amplitude increases maximum velocity

It will travel a greater distance in the same time interval; hence the maximum velocity of the oscillator will also increase

For an object moving with SHM what can be said about the total energy

The total energy remains constant as there are no losses due to frictional forces

Describe the energy changes that take place for a pendulum oscillating with SHM

At the amplitude the pendulum is briefly stationary and has zero kinetic energy. All its energy is in the form of potential energy ( in this case gravitational potential energy). As the pendulum falls it loses potential energy and gains kinetic energy. It has maximum velocity and so maximum kinetic energy as it moves through its equilibrium position. As the pendulum passes through the equilibrium position, it has no potential energy

At which position does a pendulum have maximum kinetic energy

Y

At which position does a pendulum have maximum gravitational potential energy

X

Describe the energy changes that take place for a vertical spring system oscillating with SHM

If the mass is oscillating vertically, the potential energy is in the form of gravitational potential energy (due to the position of the mass stored in the Earth's gravitational field) and elastic potential energy (stored in the spring)

Describe the energy changes that take place for a horizontal spring system oscillating with SHM

If the mass is oscillating horizontally the potential energy is in the form of elastic potential energy only

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What does it mean if we say an oscillation is damped

When an external force that acts on the oscillator has the effect of reducing the amplitude of its oscillations

Describe light damping

When damping forces are small, the amplitude of the oscillator gradually decreases either time , but the period of the oscillations is almost unchanged

Describe heavy damping

For larger damping forces the amplitude decreases significantly and the period of the oscillations also increase slightly. This type of heavy damping would occur for a pendulum oscillating in water.

Sketch a displacement time graph for and oscillator with :

What happens to the kinetic energy of the oscillator when it is damped

In all cases of damped motion, the kinetic energy of the oscillator is transferred to other forms ( usually heat)

Define the term free oscillation

When a mechanical system is displaced from its equilibrium position and then allowed to oscillate without any external forces

Define the term natural frequency

The frequency of the free oscillations is known as the natural frequency of the oscillator

Define the term forced oscillation

A periodic driver force is applied to an oscillator. In this case the object will vibrate at the frequency of the driving force ( the driving frequency)

What happens when the driving frequency of an oscillator is equal to the natural frequency of the oscillator

Explain how Barton's pendulums demonstrate resonance

Do resonance yourself I'm tired