Chapter 18 - Simple Harmonic Motion Flashcards
What are the conditions for simple harmonic motion?
- Acceleration is directly proportional to displacement
- Acceleration is in the opposite direction to displacement
a = -w²x
What type of curve is a displacement time graph?
Sine or cosine with MAX = A and MIN = -A
x = Acos (wt)
How do you plot the velocity time graph and acceleration time graph?
Velocity time graph: Plot the gradient of the displacement time graph. V = -Awsin(wt)
Acceleration time graph: Plot the gradient of the velocity time graph. a = -Aw²cos(wt)
What are the equations for maximum speed/velocity and maximum acceleration?
(In data booklet)
max V = wA
max a = w²A
What is a simple harmonic system?
Give two examples.
Simple harmonic systems are those which oscillate with simple harmonic motion, for example a simple pendulum and a mass-spring system.
What is the angle condition for a simple pendulum? Explain this.
Angle of displacement must be less than 10*, because small angle approximations are used when differentiating displacement time graphs (so this approximation is not valid for larger angles).
How is energy transferred in a simple harmonic system?
Total energy is transferred between kinetic energy and potential energy, and remains constant (when energy loss due to air resistance and heat is negligible).
For a full oscillation of a simple pendulum: Potential energy -> Kinetic energy -> Potential energy -> Kinetic energy -> Potential energy
For a full oscillation (from bottom) of a mass-spring system: Elastic potential -> Kinetic Energy -> Gravitational potential -> Kinetic energy -> elastic potential
When are potential and kinetic energy at their maximum and minimum in a simple harmonic system?
At the amplitude, potential energy is maximum and kinetic energy is zero.
At the equilibrium position, potential energy is zero and kinetic energy is maximum.
What is damping?
How does it affect amplitude?
Damping is where energy in an oscillating system is lost to the environment, reducing amplitude.
What are the three types of damping?
(See graph on RemNote for damping)
Light damping - amplitude gradually decreases by a small amount each oscillation
Heavy damping - amplitude reduces slowly without oscillating
Critical damping - amplitude reduced to zero in shortest time possible without oscillating
When do free vibrations occur?
What is the frequency?
Free vibrations occur when no external force is continuously acting on the system, meaning the system oscillates at its natural frequency?
What are forced vibrations?
Forced vibrations are where a system experiences an external driving force which causes it to oscillate at a greater frequency.
When does resonance occur?
Resonance occurs when the external driving frequency on a system is equal to the natural frequency of the system.
What is resonance?
What are some applications?
Resonance is where the amplitude of oscillations of a system drastically increase due to gaining an increased amount of energy from the driving force.
Applications include: instruments, radio, swings
How can the effect of resonance be reduced?
Damping can reduce the effect of resonance.
As the degree of damping increases, the resonant frequency decreases, the maximum amplitude decreases, and the peak of maximum amplitude widens.
(Look at graph on RemNote)
What causes damping?
Damping is caused by air resistance
What is the phase difference for forced vibrations?
When driving frequency»_space; natural frequency, displacements are out of phase by about pi radians.
When driving frequency «_space;natural frequency displacements are almost in phase.
What is the phase difference in resonance?
Displacement of driver is pi/2 radians ahead of displacement of driven system.
