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21. Advance Illustration | Simple Harmonic Motion | Average Velocity of a Particle in SHM - YouTube
Channel: Physics Galaxy
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In this illustration we'll discuss about the
average velocity of a particle in s h m. here
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we are given that a particle execute s h m
with amplitude ay and angular frequency omega
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and at t equal to zero it starts from mean
position. we are required to find the average
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velocity of particle over first 3 by 8 of
the period of s h m. and we are also required
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to find the average speed of particle in this
duration. so to understand the same. we can
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also draw. the circular motion representation
of the particle that helps in understanding
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this situation. say particle starts from,
its mean position at t equal to zero. so,
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we can calculate in time t is equal to 3 by
8 of its time period which is, 3 by 8 of time
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period we can write as 2 pie by omega if omega
is the angular frequency. this is 3 pie by,
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4 omega this is the time. the phase angle.
traversed, by particle. in s h m is. this
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phase angle, alpha we can write as omega t,
which it covers in tine t, so this omega multiplied
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by 3 pie by 4 omega, here omega gets cancelled
out this is 3 pie by 4 radian. so this position
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would be somewhere here where particle will
reach. this angle is 3 pie by 4. upto time
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t is equal to 3 by 8 of the time period. now
in this situation the particle, which is executing
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s h m would be going down, that means starting
from this position it has grown up and finally.
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it is right now located at this position.
so here we can see, in this situation, the
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particle is at a displacement we can calculate
the displacement of particle. is, y is equal
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to we are calculating at time t is equal to
3 t by 8. so this y is equal to, ay sine of,
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pie by 4, so this will be, ay by root 2, this
is the displacement of particle from its mean
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position, at time, 3 t by 8 which is 3 pie
by 4 omega. so here we can calculate the average
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velocity of particle, which is given as v
average, and it is equal to total displacement,
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upon time, so here displacement of particle
is ay by root 2. and the time as we already
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calculated it is 3 pie by 4 omega. so on,
simplifying we are getting it 2 root 2 ay
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omega. by 3 pie this is the first result of
the problem. and we can also calculate the
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average speed of particle, which is v mean.
which is scalar quantity, and distance travelled
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we need to calculate here. so average speed
is given by distance divided by time. so here
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in this duration the particle has covered
a distance 2 ay minus, ay by root 2. divided
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by the time is same which is 3 pie by 4 omega,
so on simplifying this we are getting the
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result as, 8 minus 2 root 2. ay omega by,
3 pie that will be, the result of this problem.
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