Calculating Simple Harmonic Motion Questions

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 =???