C.1 Simple Harmonic Motion

What are the two essential conditions for simple harmonic motion (SHM) to occur?

The acceleration of the object must be directly proportional to its displacement from equilibrium and directed toward that equilibrium position.

What is the defining equation for simple harmonic motion in words?

Acceleration equals negative angular frequency squared times displacement.

What is the physical significance of the minus sign in the SHM acceleration equation?

The minus sign indicates that the acceleration is always in the opposite direction to the displacement (it is a restoring force).

How is angular frequency related to the time period of an oscillation?

Angular frequency equals two times pi divided by the time period.

What is the formula for the time period of a mass-spring system?

Time period equals two times pi times the square root of the quantity mass divided by the spring constant.

What is the formula for the time period of a simple pendulum?

Time period equals two times pi times the square root of the quantity length divided by the acceleration due to gravity.

How does energy change as an oscillator moves from the equilibrium position to maximum amplitude?

Kinetic energy decreases and is converted into potential energy, while the total energy remains constant.

What does the phase angle (phi) represent in the SHM displacement equation?

The phase angle represents the starting position or the fraction of the cycle that has been completed at time zero.

What is the formula for the velocity of a particle in SHM based on its position?

Velocity equals plus or minus angular frequency times the square root of the quantity amplitude squared minus displacement squared.

How is the total energy of an SHM system calculated?

Total energy equals one-half times mass times angular frequency squared times amplitude squared.

How is the potential energy of an SHM system calculated at a specific point?

Potential energy equals one-half times mass times angular frequency squared times displacement squared.

When is the velocity of an oscillator at its maximum value?

Velocity is at its maximum when the displacement is zero (at the equilibrium position).

When is the acceleration of an oscillator at its maximum value?

Acceleration is at its maximum when the displacement is at its maximum (the amplitude).

What units must be used when calculating the phase angle in SHM?

Calculations involving the phase angle must always be performed in radians.