12.1. Simple Harmonic Motion (SHM)

• In SHM, the velocity of an object is maximum at the midpoint
• Arrange the conditions for SHM in the correct order:

  1️⃣ Restoring force is proportional to displacement

  2️⃣ Restoring force is directed towards equilibrium position

  3️⃣ No external forces other than restoring force
• In the equation for SHM, what does $\omega$ represent?


  Angular frequency
• In SHM, the period is the time taken for one complete oscillation
• The number of oscillations per unit time in SHM is called frequency
• The acceleration in SHM is always directed towards the equilibrium position.


  True
• In SHM, the acceleration of an object is proportional to its displacement and directed towards a fixed point.


  True
• SHM contrasts with uniform circular motion in the relationship between acceleration, velocity, and displacement.

  True
• The equation for acceleration in SHM is $a =$$- \omega^{2} x$
• What does the amplitude in the displacement-time graph represent?

  Maximum displacement
• The period in SHM is constant.


  True
• Simple Harmonic Motion (SHM) is a type of oscillatory motion where the acceleration is proportional to its displacement
• In SHM, the velocity is maximum at the midpoint
• The restoring force in SHM must always be directed towards the equilibrium
• Steps in deriving the SHM equation using Newton's Second Law and Hooke's Law:

  1️⃣ $ma =$$- kx$

  2️⃣ $a =$$- \frac{k}{m}x$

  3️⃣ $\omega^{2} =$$\frac{k}{m}$

  4️⃣ $a =$$- \omega^{2} x$
• What does the period of the displacement-time graph in SHM represent?

  One complete oscillation
• What does the amplitude in the displacement-time graph represent?

  Maximum displacement
• What is the direction of acceleration in SHM in relation to displacement?

  Towards equilibrium
• What does the sinusoidal shape of the displacement-time graph reflect in SHM?

  Periodic and repeating motion
• Where is the velocity zero in SHM?

  Maximum displacement points
• The equation for acceleration in SHM is $a =$$- \omega^{2} x$, where $\omega$ is the angular frequency
• Match the graphs in SHM with their corresponding properties:

  Displacement-Time ↔️ Displacement varies sinusoidally

  Velocity-Time ↔️ Velocity is maximum at midpoint

  Acceleration-Time ↔️ Acceleration is proportional to displacement
• In SHM, the equation relating acceleration and displacement is a = - ω²x
• What is the definition of amplitude in SHM?

  Maximum displacement
• In SHM, the period is dependent on the amplitude.

  False
• In SHM, the restoring force must always be directed towards the equilibrium position.


  True
• Steps to derive the equation for SHM using Newton's Second Law and Hooke's Law

  1️⃣ ma = - kx

  2️⃣ a = - (k/m)x

  3️⃣ Substitute ω² = k/m

  4️⃣ a = - ω²x
• Newton's Second Law is expressed as $F =$$ma$, and Hooke's Law is $F =$$- kx$, where $k$ is the spring constant
• In the SHM equation a = - \omega^{2} x</latex>, $\omega$ represents the angular frequency
• Match the features of the displacement-time graph in SHM with their descriptions:

  Amplitude ↔️ Maximum displacement from equilibrium

  Period ↔️ Time for one complete oscillation

  Frequency ↔️ Number of oscillations per unit time
• In SHM, the period of oscillation is constant
• In SHM, the velocity is zero at the extremes of motion.


  True
• In Simple Harmonic Motion, the acceleration is always directed towards the equilibrium position.
• The acceleration in SHM is maximum at the midpoint of the motion.

  False
• The equation for the period in SHM is $T =$$\frac{1}{f}$, where $f$ is the frequency.
• In SHM, the total energy of the system remains constant.

  True
• A mass-spring system is an example of SHM.


  True
• What type of motion is Simple Harmonic Motion (SHM)?

  Oscillatory motion
• Match the characteristic of SHM with its description:

  Acceleration ↔️ Proportional to displacement, directed towards fixed point

  Velocity ↔️ Maximum at midpoint, zero at extremes

  Displacement ↔️ Sinusoidal, repeating pattern

  Period/Frequency ↔️ Constant, independent of amplitude
• What is the defining characteristic of SHM related to acceleration and displacement?

  Proportionality