- #1
Huzaifa
- 40
- 2
Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
Is the restoring torque exactly proportional to the angle of the pendulum? What happens if the angle gets big?Huzaifa said:Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
A simple pendulum is not a perfect simple harmonic oscillator because it does not satisfy all the conditions required for simple harmonic motion. These conditions include a constant restoring force, a linear relationship between displacement and acceleration, and a constant period of oscillation. In a simple pendulum, the restoring force is not constant as it depends on the angle of displacement, the relationship between displacement and acceleration is not linear, and the period of oscillation is affected by the length of the pendulum.
No, a simple pendulum can never behave like a perfect simple harmonic oscillator because it does not satisfy all the conditions required for simple harmonic motion. However, for small angles of displacement (less than 15 degrees), the motion of a simple pendulum can be approximated as simple harmonic motion.
The length of a simple pendulum directly affects its period of oscillation, which is the time it takes for one complete back-and-forth motion. As the length of the pendulum increases, the period also increases, making it less like a perfect simple harmonic oscillator. This is because the longer the pendulum, the slower the restoring force acts on it, causing a longer period of oscillation.
Yes, there are factors that can make a simple pendulum behave more like a perfect simple harmonic oscillator. These include using a shorter pendulum, reducing air resistance, and using a material with a higher elasticity for the pendulum's string. These changes can help to make the restoring force more constant and the relationship between displacement and acceleration more linear.
Some real-life examples of simple pendulums that are not perfect simple harmonic oscillators include grandfather clocks, swing sets, and metronomes. These objects all use a pendulum for timekeeping or rhythmic motion, but their periods of oscillation are affected by factors such as air resistance and the length of the pendulum, making them imperfect as simple harmonic oscillators.