Key relationship
x=Acos(ωt+φ); v=−Aωsin(ωt+φ); a=−ω²x.
Physics · Class 11
Project circular motion into SHM
A rotating point projects onto a diameter as simple harmonic motion. The projection slows at the endpoints and is fastest at the centre. Its acceleration always points toward the equilibrium position.
Open the interactive experiment →Project circular motion into SHM
சீரான வட்ட இயக்கத்தின் விட்டத்தின் மீதான நிழல் எளிய இசை இயக்கம். முடுக்கம் எப்போதும் சமநிலை நிலையை நோக்கும்.
Key notes, relationships and model limits
Remember
A rotating point projects onto a diameter as simple harmonic motion. The projection slows at the endpoints and is fastest at the centre. Its acceleration always points toward the equilibrium position.
Common trap
SHM has variable linear speed even though the associated circular motion is uniform.
Model limits
Projection of uniform circular motion onto one diameter; schematic scales amplitude to the display. The circular particle is a mathematical model for the linear oscillator.
What you will learn
Connect circular phase with linear displacement, velocity and restoring acceleration.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
For A=1 m and ω=2 rad/s, period=π s. At x=+1 m, acceleration=−4 m/s² and velocity=0.
Why this matters
The model connects project circular motion into shm with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
At the positive maximum displacement, which way does SHM acceleration point?
- Outward, in the positive direction
- Toward the centre, in the negative direction
- Zero because velocity is zero
Read the explanation
a=−ω²x is negative when x is positive.
Course connection: Class XI Chapter 13. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.