oscillations Flashcards
SHM
the to-and-fro motion of a body about an equilibrium point
where its magnitude of acceleration is directly proportional to its magnitude of displacement
and acceleration is always directed towards the equilibrium position/acceleration and displacement are in opposite directions
how do uk object is moving in SHM?
a= -(k/m) x
k/m is a constant -> acceleration is directly proportional to the displacement
negative sign shows that acceleration and displacement are in opposite directions
displacement of an oscillating body
linear distance from its equilibrium position at any instant in time
amplitude
max displacement of the oscillating body
period
time taken for one complete oscillation
frequency
no. of complete oscillations per unit time
angular frequency
rate of change of angular displacement (in radians) per unit time
phase difference
fraction of a cycle by which one oscillation is ahead of behind eo
phase diff = angular velocity (t2-t1)
what happens if object is damped
when object is subjected to frictional or other dissipative forces which opposes motion
total mechanical energy decreases over time as work is done against the forces
amplitude decreases over time
light damping
amplitude decreases exponentially with time
period is slightly larger and remains constant with time
higher degree of light damping
amplitude decreases exponentially with time more rapidly
period increases slightly
critical damping
system returns to equilibrium W/O OSCILLATING in the shortest possible time -> strong dissipative forces
heavy damping
system takes a very LONG TIME to return to equilibrium position W/O OSCILLATING-> strong dissipative forces
why free oscillation oscillate at natural frequency
- no external periodic driver -> cant provide energy continuously
- no resistive force to cause damping -> amplitude remains constant
forced oscillations
- maintained by an external periodic driver -> energy is constantly supplied
- driving system oscillates at driving freq of the external periodic driver
rs btwn amplitude and energy
energy supplied>energy loss (bc of damping)
-> amplitude increases
energy supplied=energy loss
-> amplitude remains the same
resonance
phenomenon exhibited by a driven system acted upon by an external periodic driver continuously
-> occurs when driving frequency approaches natural frequency of driven system/equal to resonant frequency of the driven system
-> maximum energy transfer
-> driven system has maximum amplitude
amplitude of driven system increases when..
degree of damping decreases
difference between natural frequency and driving frequency increases
magnitude of force increases
when degree of damping increases..
amplitude of driven system decreases
resonant frequency decreases
