★motion
motion is the phenomenon in which object changes its position over time
is described by
- displacement, distance.
- velocity, speed.
- Acceleration.
- Time.
– Types of motion.
Rotational mation
Linear motion
oscillatory motion
Resp Res ting Cupidon, b
- Acceleration.
Rate of change of velocity per unit time.
- velocity
Rate of change of displacement per unit time.
unit = m/s
-where 5 is distance
t is time
– where t is time U is velocity
- unit = m/s
periodic motion.
Any motion which repeats itself an after define introvert of time is called periodic motion,
i.e uniform circular motion, oscillatory, liberation motion
period and periodic mation.
A body is an Perfoming periodic motion goes repeating the some set of movement, the time taken bor its one such movement. period or periodic time. is called.
Simple Harmonic motion (SHM).
-Im Simple harmonie notion. linear Periodic motion which force is directed position and proportional to mean is defined the of the body, in to ward the mats mean is magnitude is directly to the displacement position. from the mean position.
The course’s preis process gone os Ale black side of its mean position, strength puth progressing that to oscillate equilibrium position either such escalation motion in called simple harmonie motion.
oscillations.
oscillation is defined as the processor repeats variations of Any quantity or measure equilibrium volve in time.
OR
oscillations refers to any periodic motion moving to a distance about the equilibrium position and report it sells and over for a period of time.
Note:-
→ Every oscillatory motion is periodic but every Periodic motion need not be oscillatory.
Extreme value of displacement(x), velocity(v), and acceleration(a).
Displacement :-
displacement The general expression for S.H.M is x=A sin 1 (cot + theta)
At mean position (wt + theta) = 0 06 ㅠ
at mean position dis placement. is minimum.
i.e zero.
At extreme position (wt + phi) 9/2 37/2
: x = A * sin(omega*t + phi)
x = plus/minus b * ln(pi/2)
extreme position displacement is maximum.
X max = -+A
Velocity (v).
The general expression for velocity (v) is
v = plus/minus omega * sqrt(A ^ 2 – x ^ 4)
At mean position, x=0 v mas = pm beta w
Le the velocity is maximum at meas position
# At extreme position, x = plus/minus A.
v min 1 = 0
Le the velocity is minimum at extreme position.
Acceleration .
The acceleration of a particle is
at mean position x = 0 , q min =0
Le acceleration is minimam at nem position
# at extreme position X = IA g AAF = pm omega A ^ 2
La acceleration.
in maximum at extreme position.
Amplitude.
displacement ob brom the The minimum S.H.M 3 particle performing mean position is collect amplitude.
Hero, displacement of particles performing S.H.M x= Asin (wt)
For maximum displacement sin (wt+6)=1
i.e x=plus minus A .That nis nothing but Amplitude.
Frequency of S.H.M.
The number of oscillations performing by particle is called performing the S.H.M par unit time is called the frequency.
n= 1/T
Simple pendulum :-
An ideal simple pendulum. Suspended by a string trom a is a heavy particle massless, inextensible, flexible rigid support.
A practical Simple
Pendulum is a small heavy (dense) sphere called bob suspended by a light. and inextensible string.
The distance between point Suspension gravity of and contrary of the bob called length.
Tension In Tin the string the placed position (extreme position).
1)Force I due to directed along the tension String. in the string.
2)weight mg in the vertically down word direction.
Angular oscillation turigional oscillation.
metallic (nylon or dise attached aito thin metallic wire) hanging bram Suppert If the list is about the. Released, Partly in it were rigid slightly twisted axis along the wire performs on rotational mutien clockwise and anticlockwise Sense such oscillation are called angular oscillations original oscillation.
Free oscillation.
If an object is allowed to oscillate vibrate on its own, it does so with its natural frequency.
For example, if the bub of a Simple pendulum of length & is displaced and released oscillate only with the frequency what is called its natural frequency and. the oscillations or free oscillation.
Forced oscillation.
By applying periodic force the some pendulum. can be made to oscillate with different frequency.
The oscillation will be forced oscillations.
