Articles by "a simple harmonic motion"
Tampilkan postingan dengan label a simple harmonic motion. Tampilkan semua postingan

di 0
In previous lessons we spoke about simple harmonic motion, its definition, systems that engage in simple harmonic motion and formulas involved. Now we’ll be looking at calculating Simple harmonic motion questions.

Example # 1

S.H.M

In the diagram above a particle is moving with S.H.M with a period of 24 seconds between two points A and B. Find the time taken to travel from:
a) A to B
b) O to B
c) O to C
d) D to E

Answers:
Note that the period is the time taken to complete one revolution in this case the period is the time taken for the particle to travel from A to B and then to A again (24 seconds as stated in the question above).

a) A to B
A to B is half a period which would be = 12 second

If you want to work this question in a more detailed way, you can do this:

Distance from A to B to A again = 16m
Distance from A to B = 8m
Period (A to B to A again) = 24 seconds
Time (t) from A to B =???



b) O to B
O to B is quarter of the period so the answer would be = 6 sec

Or you can follow the above pattern:

Distance from A to B to A again = 16m
Distance from O to B = 4m
Period (A to B to A again) = 24 seconds
Time (t) from O to B =???












c) O to C
This is one eight of the period which would be = 3 seconds

Or by detailed calculation:

Distance from A to B to A again = 16m
Distance from O to C = 2m
Period (A to B to A again) = 24 seconds
Time (t) from O to C =???













d) D to E
Note with this question, if you observe the diagram carefully you will see that you weren’t given the distance between D to E directly. However this can easily be found by subtracting the distance O to D from the distance O to E and this would give you the distance from D to E.

Distance from A to B to A again = 16m
Distance from D to E = 3.5 – 3 = 0.5m
Period (A to B to A again) = 24 seconds
Time (t) from D to E =???












Continue reading

di 0
What is Simple Harmonic Motion?
Simple Harmonic Motion can be defined as the motion of an object where its acceleration is directly proportional to its distance from a fixed point along a path. The acceleration is said to always be directed towards the fixed point. This fixed point is known as the equilibrium position; this is because it is where the object that is swinging freely would come to rest given that it has lost all its energy.

The diagram below shows a pendulum in simple harmonic motion:
Pendulum in S.H.M


Where:
P is the equilibrium position (where the body would come to rest)
PQ & PR gives the amplitude position which is the greatest displacement from equilibrium position.
X is the position from the equilibrium position.

When the object is swinging freely you’ll probably realize that it moves faster when passing through its equilibrium position P, this is because the body’s acceleration and velocity is greatest as it passes through the equilibrium position. Also the opposite happens as the body leaves the equilibrium position, the acceleration and velocity lessens as the body’s position, x, moves further away from the equilibrium position.

Formulas involved in simple harmonic motion:

S.H.M formulas


The diagram below shows a spring in simple harmonic motion:
Spring in S.H.M

Continue reading
Langganan: Postingan (Atom)