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Oscillations and Waves Topic 4.1 Kinematics of simple harmonic motion (SHM)
Examples of oscillations ,[object Object],Nature of oscillating system p.e. stored as k.e. possessed by moving Mass on helical spring Elastic energy of spring Mass cantilever Elastic energy of bent rod Rod Simple pendulum Gravitational p.e. of bob Bob Vertical rod floating in liquid of zero viscosity Gravitational p.e. of rod or liquid rod
Displacement ,[object Object],[object Object],O B A P
Amplitude & Period ,[object Object],Ball A ,[object Object],Ball A ,[object Object]
Frequency ,[object Object],[object Object],f = 0.0833 Hz
Angular frequency ,[object Object],[object Object],Ball B
[object Object],Find the: Amplitude Period Frequency Angular frequency 10 cm 0.2 s 5.0 Hz 10   rads -1
Phase ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Phase This information concentrates on what  phase  of the cycle is being executed. It is not concerned with the particulars of amplitude. Mathematically, the phase is the "w t" in:   x(t) = A cos (   t)
Phase ,[object Object],Recall: x(t) = A cos (   t)   What phase is the ball in when:  x = 0, v < 0  A. 0.00    rad  B. 0.25    rad  C. 0.50    rad  D. 1.0    rad  E. 1.5    rad  F. 1.7    rad
Phase ,[object Object],Recall: x(t) = A cos (   t)   What phase is the ball in when:  x = +A, v = 0  A. 0.00    rad  B. 0.25    rad  C. 0.50    rad  D. 1.0    rad  E. 1.5    rad  F. 1.7    rad
SHM and circular motion Uniform Circular Motion  (radius A, angular velocity w)  Simple Harmonic Motion  (amplitude A, angular frequency w) ,[object Object],[object Object]
Velocity and acceleration ,[object Object],x(t) = A cos (  t +   )  ,[object Object],v(t) = -A    sin (  t +   )  ,[object Object],[object Object],[object Object],a(t) = -A   2  cos (  t +   )  ,[object Object],[object Object]
Velocity and acceleration ,[object Object],[object Object],[object Object],[object Object],C A and E
Velocity and acceleration ,[object Object],[object Object],[object Object],[object Object],A and E C
Summary 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Questions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Questions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary 3 ,[object Object],In terms of time In terms of displacement Displacement Velocity Acceleration
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Simple pendulum ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],W T θ
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Oscillations and Waves Topic 4.2 Energy changes during SHM
[object Object]
Mass on spring resonance ,[object Object],the expression for the resonant vibrational frequency: This kind of motion is called simple harmonic motion and the system a simple harmonic oscillator.
Mass on spring: motion sequence ,[object Object]
Energy in mass on spring ,[object Object]
Potential energy At extension x:
Kinetic energy At extension x:
Total energy Total energy
Oscillations and Waves Topic 4.3 Forced oscillations and resonance
Damped oscillations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Total energy E / J Time / s Energy of system Total energy E / J Time / s Dissipated energy
Damping ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Types of damping 1 ,[object Object],[object Object],t/s x/m
Types of damping 2 ,[object Object],[object Object],t/s x/m T/4
Types of damping 3 ,[object Object],[object Object],t/s x/m Very slow return to zero displacement
Natural oscillations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Forced oscillations ,[object Object],[object Object],[object Object]
Effects of forced oscillations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Resonance ,[object Object],[object Object],[object Object],[object Object]
Useful resonance ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
When resonance goes bad ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Tacoma Bridge
Movie
Circular Motion ,[object Object],[object Object],[object Object]
Vector Diagrams uniform speed velocity at a tangent Acceleration and  force directed  towards the centre
Centripetal Acceleration ,[object Object],[object Object],[object Object],[object Object],[object Object]
Centripetal Force ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
SHM ,[object Object],[object Object],[object Object],[object Object]

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Simple Harmonic & Circular Motion