Oscillations Flashcards
what is periodic motion
A motion that repeats itself at regulat intervals of time is said to be periodic motion. Eg: pendulum of a clock
what is oscillatory motion
when a body eecutes to and fro motion in regular interval of time, it is is said to perform oscillatory motion.\
all oscillations are periodic but not all periodic motion is oscillatory
when the frequency of oscillation is very high, it is called as a vibration. eg strings of a guitar
what causes oscillatory motion
the body undergoing periodic
motion has an equilibrium position somewhere
inside its path. When the body is at this position
no net external force acts on it. Therefore, if it is
left there at rest, it remains there forever. If the
body is given a small displacement from the
position, a force comes into play which tries to
bring the body back to the equilibrium point,
giving rise to oscillations or vibrations.
define:
i) time period
ii) frequency
iii)displacement
iv) amplitude
i) time taken to complete 1 oscillation
ii) the no of oscillations performed in 1 second
iii) the distance travelled by the oscillating particle at any instant from its mean/ equilibrium position. It may be expressed in terms of length or angle, depending upon the body in consideration.
iv) the maximum value of displacement of a particle is called as amplitude.
what functions are periodic
functions that repeat itself at regular intervals are periodic. Any
periodic function can be expressed as a
superposition of sine and cosine functions
of different time periods with suitable
coefficients.
sine and cosine functions repeat at intervals of 2π
logarithmic and exponential functions are not periodic functions as they dont repeat themselves at regular intervals. The function e
–ωt
is not periodic, it
decreases monotonically with increasing
time
(iv) The function log(ωt) increases
monotonically with time t. It, therefore,
never repeats its value and is a nonperiodic function.
what is simple harmonic motion
Simple harmonic motion is the simplest form
of oscillatory motion. This motion arises when
the force on the oscillating body is directly
proportional to its displacement from the mean
position, which is also the equilibrium position.
Further, at any point in its oscillation, this force
is directed towards the mean position.
what are the energies possessed by a body in shm
(i) kinetic energy is possessed by the body as a virtue of its motion.is also a periodic function of time, being zero
when the displacement is maximum and
maximum when the particle is at the mean
position. Note, since the sign of v is immaterial
in K, the period of K is T/2.
ii)potential snergy is possesed by the body due its displacement against restoring force.the potential energy of a particle
executing simple harmonic motion is also
periodic, with period T/2, being zero at the mean
position and maximum at the extreme
displacements.
what are linear and non linear oscillators
Note that the force in Eq. (13.13) is linearly
proportional to x(t). A particle oscillating under
such a force is, therefore, calling a linear
harmonic oscillator. In the real world, the force
may contain small additional terms proportional
to x
2
, x
3
, etc. These then are called non-linear
oscillators.
What is phase of an oscillating body
Phase of an oscillating body at any instant fully expresses its position and direction of motion wrt mean position at that instant.
For an oscillating body with a sine or cosine function phase is the argument kf the function
What is epoch/ phase constant/ initial phase
It represents the phase of the body when t=0.
What is epoch/ phase constant/ initial phase
It represents the phase of the body when t=0.
What is force law for SHM
Restoring force for simple harmonic motion is directly proportional to displacement and directed towards the mean position
SHM and UCM
The projection of the reference particle performing uniform circular motion on any of its diameters is called SHM. The circle is called reference circle
What is simple pendulum
Simple pendulum consists of a heavy point mass suspended from a light inextrnsible flexible string from a rigid support about which is free to oscillate
