6.1 Periodic motion

• The formula for the period of periodic motion is T = 1/f
• Simple Harmonic Motion (SHM) occurs when the restoring force is proportional to the displacement
• The angular frequency in SHM is given by the formula ω = √(k/m)
• What is the equation for acceleration in SHM?

  $a =$$- \omega^{2} x$
• The angular frequency in SHM is related to the frequency \( f \) by the formula \omega = 2\pi f
• The angular frequency in SHM is measured in radians per second.
• In SHM, acceleration is directly proportional to displacement and angular frequency squared.
• What is the relationship between period and frequency in SHM?

  Inversely proportional
• What is the formula for angular frequency in SHM?

  $\omega =$$\sqrt{\frac{k}{m}}$
• The period in SHM is the time taken to complete one full cycle of motion.

  True
• The period of SHM is the time taken to complete one full cycle of motion

  True
• Kinetic energy in SHM is maximum at the equilibrium position


  True
• The total energy in SHM remains constant
• Match the type of damping with its description:

  Underdamped ↔️ Oscillations decrease gradually

  Overdamped ↔️ No oscillations, returns to equilibrium

  Critically Damped ↔️ Returns to equilibrium without oscillating
• Resonance occurs when the frequency of the external force matches the system's natural frequency.
• Periodic motion is any motion that repeats itself in equal intervals of time
• Frequency is measured in Hertz (Hz).


  True
• In SHM, the restoring force is always directed towards the equilibrium position.


  True
• The displacement in SHM is given by the equation $x =$$A \cos(\omega t + \phi)$.


  True
• Periodic motion is characterized by cycles completed per unit time, known as frequency.


  True
• The restoring force in SHM is always directed towards the equilibrium position.


  True
• The restoring force in SHM is always directed towards the equilibrium position.


  True
• Steps to derive the velocity and acceleration equations in SHM

  1️⃣ Start with the displacement equation

  2️⃣ Take the first derivative to find velocity

  3️⃣ Take the second derivative to find acceleration
• Periodic motion is any motion that repeats itself in equal intervals of time.
• In the displacement equation of SHM, φ represents the phase angle.
• What does the amplitude in the displacement equation of SHM represent?

  Maximum displacement
• Match the property with its correct formula:

  Period (T) ↔️ $T =$$\frac{1}{f}$

  Frequency (f) ↔️ $f =$$\frac{1}{T}$
• The formula for kinetic energy is $KE =$$\frac{1}{2}mv^{2}$
• Damping in SHM reduces the amplitude of oscillations over time

  True
• Order the types of damping from weakest damping force to strongest damping force:

  1️⃣ Underdamped

  2️⃣ Critically Damped

  3️⃣ Overdamped
• Resonance leads to a large increase in the amplitude of oscillations


  True
• A complete cycle of periodic motion is called a period.

  True
• What is the formula for frequency in terms of period?

  $f =$$\frac{1}{T}$
• Match the property with its definition:

  Restoring Force ↔️ Force pulling the object back to equilibrium

  Amplitude ↔️ Maximum displacement

  Angular Frequency ↔️ Rate of oscillation in radians/second
• The velocity in SHM is given by the equation v = -Aω sin(ωt + φ)
• Match the SHM property with its correct formula:

  Restoring Force ↔️ F = -kx

  Angular Frequency ↔️ $\omega =$$\sqrt{\frac{k}{m}}$
• What is the definition of restoring force in SHM?

  Force pulling object to equilibrium
• What does the phase angle φ represent in the displacement equation of SHM?

  Initial position
• Match the property of SHM with its formula:

  Period ↔️ $T =$$\frac{1}{f}$

  Frequency ↔️ $f =$$\frac{1}{T}$
• In SHM, the restoring force is directly proportional to the displacement and acts in the opposite direction.

  True