CAPF AC 2020 Q4: Science & Technology – Physics
- (a) All the periodic motions are necessarily simple harmonic
- (b) All the simple harmonic motions are necessarily periodic motions
- (c) There is no co-relation between the simple harmonic motions and the periodicity of motion
- (d) The relation between the simple harmonic motion and periodic motion depends upon the mass of object undergoing the motion
Answer: (b) All the simple harmonic motions are necessarily periodic motions
Explanation
Periodic motion and simple harmonic motion
How to think: draw two circles, one inside the other.
SHM is the small circle inside the big circle of periodic motion.
Everything in the small circle is in the big one, but not the other way round.
Periodic motion is any motion that repeats after a fixed time.
Simple harmonic motion (SHM) is a special periodic motion.
In SHM the restoring force is proportional to the displacement and points towards the mean position.
| Motion | Periodic? | Simple harmonic? |
|---|---|---|
| Mass on a spring | Yes | Yes |
| Simple pendulum, small swing | Yes | Yes (approximately) |
| Earth going around the Sun | Yes | No |
| Hands of a clock | Yes | No |
The options checked:
| Option | Verdict |
|---|---|
| (a) All the periodic motions are necessarily simple harmonic | Incorrect; the Earth's revolution is periodic but not SHM |
| (b) All the simple harmonic motions are necessarily periodic motions | Correct |
| (c) There is no co-relation between the two | Incorrect; SHM is one kind of periodic motion |
| (d) The relation depends upon the mass of the object | Incorrect; mass changes the time period, not the kind of motion |
Answer: (b) All the simple harmonic motions are necessarily periodic motions.
Why each option is right or wrong
- (a) Incorrect. The Earth's revolution is periodic but not simple harmonic.
- (b) CORRECT. Every simple harmonic motion repeats itself, so it is periodic.
- (c) Incorrect. There is a clear relation: SHM is a special case of periodic motion.
- (d) Incorrect. Mass affects the time period; it does not decide whether the motion is periodic.
Key point
Every simple harmonic motion is periodic, but not every periodic motion is simple harmonic. SHM needs a restoring force proportional to displacement.
Remember
All SHM is periodic; all periodic motion is not SHM.
Common mistakes
- Reading the statement backwards and marking all periodic motions are simple harmonic.
- Treating uniform circular motion as simple harmonic; only its projection on a diameter is.
- Forgetting that a pendulum is simple harmonic only for small swings.
Exam tip
Educated guess: (a) and (b) are the same sentence turned around. The Earth going round the Sun is periodic but not SHM, so (a) falls.
Sources
- NCERT Class XI Physics — Oscillations
- NCERT Class IX Science — Sound (oscillation and time period)