Simple harmonic motion is an oscillation where the force on a body is always directed towards a fixed point, and is proportional to the body's displacement from the fixed point.

i.e. the 3 main requirements for simple harmonic motion of a mechanical system are:

1) A mass that oscillates

2) A central position where a mass is in equilibrium

3) A restoring force

[image]They are all sinusoidal curves. When x is zero it is at the mid point of its oscillation so v is at its maximum. a is the gradient of the V against time graph.

Q1) Define frequency

Q2)How many ∏ radians is a complete cycle of simple harmonic motion?

Q3)What it the equation for angular frequency?

A1) The frequency is the number of oscillations made per unit time. f=1/T

A2)There are 2∏ radians in a complete cycle of simple harmonic motion

3) w=2∏f of w=2∏/T

Q1)In simple harmonic motion, displacement can be represented as a function of time by which 2equations?

Q2) What do the x and A stand for in these equations?

Q3) When would you use the sine vesion of the equation and when would you use the cos version?

Q4) What must your calculator be working in to calculate (2∏ft)?

Q5) Write the equations showing acceleration and velocity as a function of time.

A1) x= A sin (2∏ft) and x= A cos (2∏ft)

A2) x is the displacement and A is the maximum displacement or amplitude

A3) Use the sin version when x=0 and t=0 at the start of the oscillation. Use the cos version when x=A at t=0.

Q4) Radians

Q5) a=-a_maxcos(2∏ft)

v=-v_maxsin (2∏ft)

In simple harmonic motion, what is acceleration proportional to?

Write the equation relating these things.

In simple harmonic motion, acceleration is proportional to displacement from a fixed point, and is directed towards that point

a=-w²x

or

a=-(2∏ft)²x

Q1)In simple harmonic motion, there is a regular interchange between which types of energy?

Q2)When does the system have the maximum of each type of energy?

Q3)What happens to the total energy of the system, provided the oscillations are undamped.

                                          A1)In [image]simple harmonic motion, there is a regular interchange between kinetic and potential energy.

A2) A system has the most potential energy at maximum displacement e.g when a spring is pulled to one side it is being stretched. A system has the most kinetic energy at x=0. e.g. when the spring has accelerated back to the central position.

A3) The total energy of the system remains constant because as kinetic energy increases potential energy decreases and vice versa.

What is damping?

What is the difference between light, heavy and critical damping?

Where is damping used?

[image]Damping is when the amplitude of oscillation decreases over time because a resistive force has been introduced which removes energy from the system. Light damping is when the amplitude decreases exponentially over time.  In heavy damping, no oscillation occurs. In critical damping the oscillating mass returns to rest in the shortest possible time, without any oscillation.

Damping is used in the suspension of cars to make  the ride less bumpy!

Q1)What is the natural frequency of vibration?

Q2)What is resonance?

A1) The natural frequency of vibration is the frequency at which an object will vibrate when it is allowed to do so freely.

A2) Resonance is a phenomenon that occurs when the frequency at which and object is forced to vibrate is equal to its natural frequency of vibration. The amplitude of vibration is at its maximum at this frequency .

Q1)When can resonance be a problem?

Q2) When can resonance be useful?

A1)

• Bridge building e.g. Tacoma Narrows in Washington State USA collapsed in a mild gale in July 1940. The wind set up oscillating vortices around the air which vibrated more and more violently until it broke up under stress.
• Earthquakes- buildings are forced to oscillate by the vibrations of the earth.

A2)

• Musical instruments
• Microwave cooking- the microwaves used have a frequency that matches the natural frequency of vibration of the water molecules.
• Magnetic Resonance Imaging (MRI)- A computer generated image can be produced by analysing the absorption of radio waves by atomic nuclei.
• Radio and TV- The tuner can be adjusted to resonate at the frequency of the station you are interested in, and the circuit produces a large-amplitude signal for this frequency only.