Question

Model the motion of a meter stick suspended from one end on a low-friction. Do not make the small-angle approximation but allow the meter stick to swing with large angels. Plot on the game graph both$\theta$and the $z$component of $\overrightarrow{\omega }$vs. time, Try starting from rest at various initial angles, including nearly straight up (Which would be ${\theta }_i=\pi$ radians). Is this a harmonic oscillator? Is it a harmonic oscillator for small angles?

Short answer

This does not correspond to a harmonic oscillator; it behaves almost like a harmonic oscillator for small angular oscillations.

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The initial angle is zero.

• The second angle is, ${\theta }_i=\pi$.

Significance of angular speed

A physical system whose values fluctuate above and below the average value at one or more characteristic frequencies.

Determination of the relative kinetic energy

If large angular vibrations are allowed, this measuring rod or compound pendulum will move in harmony. This means that both offsets of the average position are not equal.

The below graph shows the$\theta$vs $t$and ${\omega }_z$vs$t$.

Here ${\theta }_i=0$and displacements are not equal.

Here ${\theta }_i=\pi$displacements are not equal.

This does not correspond to a harmonic oscillator; it behaves almost like a harmonic oscillator for small angular oscillations. Because there is less friction, the amplitude decreases over time but maintains harmonic oscillations.