shm Flashcards
give an example of simple harmonic motion
vibrating string of a musical instrument, a pendulum, AC flowing through a wire, atoms in a molecule vibrate with shm
define simple harmonic motion
the motion of an oscillator where its acceleration is directly proportional to its displacement from its equilibrium position and is directed towards that position
define natural frequency
the unforced frequency of a freely oscillating object ie. a plucked guitar string will continue to oscillate after it is released, the frequency at which it continues to oscillate is its natural frequency
the three conditions that make an oscillation simple harmonic
- the acceleration is always towards the equilibrium
- the acceleration is directly proportional to displacement from equilibrium position
- the time period is independent of the amplitude (isochronous)
name the different graphs (sine or cosine) that apply to displacement, velocity, acceleration and force of simple harmonic motion
displacement- sin graph
velocity- cos graph
acceleration- negative sin graph
force- negative sin graph
define period
the time taken for one full oscillation (unit: seconds (s))
define frequency
the amount of oscillations per unit time (unit: hertz (Hz))
define angular frequency
the rate of change of angle expressed in radian per second
define equilibrium
the tension in the spring is equal and opposite to the weight of the mass
explain the transfer between kinetic and potential energy in an oscillating system
when the mass is released potential energy decreases due to it converting to kinetic energy. At the bottom of the pendulum (equilibrium position) all the energy is kinetic
define resonance
the forced motion of an oscillator characterised by maximum amplitude when the forcing frequency matches the natural frequency of the oscillator. A system absorbs maximum energy when the source frequency is equal to the natural frequency of the system
describe the effects of damping on an oscillatory system
a system which does not continue oscillating due to an external force, such as friction. The amplitude of damped oscillations decays exponentially with time. Introducing damping removes some of the energy from the oscillating system
list some uses of resonance
MRI scans, microwaves, tuning a TV or radio, musical instruments
what three statements apply to a system in resonance
- its natural frequency is equal to the frequency of the driver
- its amplitude is maximum
- it absorbs the greatest possible energy from the driver
how does damping effect resonance
as the degree of damping is increased, the amplitude of the resonant vibrations decreases, the resonance peak becomes broader and the frequency gets slightly lower
