7.2 Frequency and Period of SHM

• The negative sign in the SHM restoring force formula indicates that the force acts in the same direction as the displacement.

  False
• The unit of frequency is Hertz (Hz), which equals one cycle per second.


  True
• Match the characteristic with the correct term:

  Time to complete one cycle ↔️ Period

  Number of cycles per unit time ↔️ Frequency
• In SHM, the restoring force acts in the same direction as the displacement.

  False
• What is the unit of frequency?

  Hertz (Hz)
• Period is the time it takes for an object to complete one full cycle
• The frequency of a pendulum with a period of 4 seconds is 0.25 Hz
• Simple Harmonic Motion (SHM) occurs when the restoring force is directly proportional to the object's displacement
• Frequency is the number of complete cycles or oscillations per unit of time
• The period of SHM is measured in seconds.


  True
• What does 'k' represent in the formula F = -kx?

  Spring constant
• Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to its displacement
• Frequency and period are inversely related in SHM.

  True
• Frequency is measured in seconds.

  False
• The number of complete cycles per unit time is called frequency
• The period in SHM is inversely related to the angular frequency
• What is the restoring force in SHM expressed mathematically?

  $F =$$- kx$
• What is the formula for the period $T$ in SHM in terms of mass $m$ and spring constant $k$?


  $T =$$2\pi \sqrt{\frac{m}{k}}$
• One key characteristic of SHM is that the restoring force is proportional to the displacement
• Frequency is measured in Hertz, where 1 Hz equals one cycle per second.
• The period $T$ is inversely related to the frequency f</latex> by the formula $T =$$\frac{1}{f}$. This means that if the frequency increases, the period decreases.
• Match the characteristic with the type of motion:

  Restoring Force is proportional to displacement ↔️ SHM

  Path follows complex, non-repeating curves ↔️ Non-SHM
• The formula for frequency is $f =$$\frac{1}{T}$, where $T$ is the period
• The restoring force in SHM is mathematically expressed as F = -kx
• Match the characteristic with the type of motion:

  Restoring force proportional to displacement ↔️ Simple Harmonic Motion

  Restoring force may not be zero at equilibrium ↔️ Non-SHM
• What is the formula for period in terms of frequency?

  $T =$$\frac{1}{f}$
• Match the characteristic with its correct unit:

  Frequency ↔️ Hertz (Hz)

  Period ↔️ Seconds (s)
• Frequency and period are inversely proportional in oscillatory motion.


  True
• In SHM, the angular frequency is $\omega =$$\sqrt{\frac{k}{m}}$.


  True
• The period $T$ is inversely related to the angular frequency $\omega$ by the formula $T =$$\frac{2\pi}{\omega}$. The angular frequency is measured in radians per second
• The angular frequency $\omega$ in SHM is expressed as $\omega =$$\sqrt{\frac{k}{m}}$. This formula depends on the spring constant $k$ and the mass
• What type of motion is Simple Harmonic Motion (SHM)?

  Periodic motion
• What type of curves does the motion in SHM follow?

  Sine or cosine curves
• Period is the time it takes for an object to complete one full cycle of oscillation.


  True
• Match the units with their corresponding physical quantities:

  Frequency ↔️ Hertz (Hz)

  Period ↔️ Seconds (s)
• What is frequency measured in?

  Hertz
• The period of an oscillation is measured in seconds.


  True
• The period in SHM depends only on the spring constant k</latex>.

  False
• If a pendulum completes one full swing in 4 seconds, its frequency is 0.25 Hz.

  True
• What is the unit of period?

  Seconds (s)