11 - Simple Harmonic Motion Free Online FlashCards

What condition defines simple harmonic motion?

Simple harmonic motion occurs when the restoring force is proportional to displacement and directed toward equilibrium: $F_x=-kx$.

What is a stable equilibrium position?

The equilibrium position is where the net force is zero. A stable equilibrium also produces a restoring force when the system is displaced.

What does amplitude mean in SHM?

Amplitude $A$ is the maximum displacement from equilibrium, so the object moves between $x=+A$ and $x=-A$.

How are period and frequency related?

The period is the time for one complete oscillation, while frequency is the number of oscillations per unit time: $f=\frac{1}{T}$.

What is the angular frequency of an oscillator?

Angular frequency is $\omega=2\pi f=\frac{2\pi}{T}$, measured in radians per second.

What does the phase constant determine?

For $x(t)=A\cos(\omega t+\phi)$, the phase constant $\phi$ determines the oscillator’s position in its cycle at a given time.

Where is an SHM oscillator fastest?

The speed is greatest at equilibrium, where $x=0$, and the velocity is zero at the turning points, where $x=\pm A$.

Where is SHM acceleration greatest?

The magnitude of acceleration is greatest at the turning points and zero at equilibrium, because $a=-\omega^2x$.

How does spring-oscillator energy depend on amplitude?

For a spring oscillator, total mechanical energy is $E=\frac{1}{2}kA^2$. Therefore, doubling the amplitude makes the energy four times greater.

How is energy distributed at equilibrium in a spring oscillator?

At a spring oscillator’s equilibrium position, spring potential energy is zero and kinetic energy is maximum. At either turning point, kinetic energy is zero and spring potential energy is maximum.

What determines a mass–spring period?

The mass–spring period is $T_s=2\pi\sqrt{\frac{m}{k}}$. Increasing $m$ increases the period, while increasing $k$ decreases it.

What is the small-angle period of a simple pendulum?

For small angular displacements, a simple pendulum has period $T_p=2\pi\sqrt{\frac{\ell}{g}}$.