5.3. Simple Harmonic Motion (SHM)

• What is Simple Harmonic Motion (SHM)?

  A type of oscillatory motion
• Match the characteristic of SHM with its description:

  Acceleration ↔️ Proportional to displacement, directed towards fixed point

  Velocity ↔️ Reaches maximum at midpoint, zero at extremes

  Displacement ↔️ Sinusoidal, repeating pattern

  Period ↔️ Time taken for one complete oscillation
• What is the first condition for SHM?

  Acceleration proportional to displacement
• What does the term 'A' represent in the displacement equation of SHM?

  Amplitude
• What does the variable φ represent in SHM equations?

  Phase constant
• The acceleration in SHM is proportional to the square of the angular frequency.


  True
• What is the frequency (f) in SHM defined as?

  Oscillations per unit time
• In the displacement graph of SHM, the amplitude represents the maximum displacement.
• Match the energy type with its description in SHM:

  Kinetic Energy ↔️ Maximum at midpoint

  Potential Energy ↔️ Maximum at extremes
• In general oscillatory motion, the acceleration is always proportional to the displacement.

  False
• The acceleration in SHM is always directed away from the fixed point.

  False
• In SHM, velocity reaches its maximum at the equilibrium position.


  True
• How is the period (T) related to the angular frequency (ω)?

  $T =$$\frac{2\pi}{\omega}$
• The displacement graph in SHM is a sinusoidal pattern with the amplitude representing the maximum displacement
• In SHM, the total energy remains constant due to the conservation of energy
• Kinetic energy in SHM is maximum when the object is at its equilibrium position.


  True
• What happens to the amplitude of oscillations during resonance?

  Increases significantly
• In SHM, the velocity is maximum at the equilibrium position and zero at the extremes.


  True
• For SHM, the acceleration must be proportional to the object's displacement
• In SHM, the velocity is given by the equation v = - \omega A \sin(\omega t + \phi)</latex>, where 'v' represents the object's velocity
• What is the period (T) in SHM defined as?

  Time for one oscillation
• What type of graphs are used to represent the motion of an object in SHM?

  Displacement, velocity, acceleration
• The acceleration graph in SHM is the second derivative of the displacement graph.


  True
• Simple Harmonic Motion is a type of oscillatory motion where the acceleration is proportional to the object's displacement.
• What does the equation $a \propto - x$ represent in SHM?


  Proportional acceleration
• The angular frequency in SHM is measured in radians per second.


  True
• What is the equation for velocity in SHM?

  $v =$$- \omega A \sin(\omega t + \phi)$
• The period in SHM is the time taken for one complete oscillation
• How is the frequency (f) related to the period (T)?

  f = \frac{1}{T}</latex>
• What is the relationship between the graphs of displacement, velocity, and acceleration in SHM?

  Derivative relationship
• What is the maximum value of potential energy in SHM?

  $PE_{\max} =$$\frac{1}{2}kA^{2}$
• The equation for damped oscillations includes a damping coefficient denoted by b
• In SHM, the acceleration is proportional to the object's displacement
• Arrange the conditions for SHM in their logical order:

  1️⃣ Acceleration must be proportional to displacement

  2️⃣ Acceleration must be directed towards the fixed point
• In SHM, the acceleration must always be directed towards the fixed point.


  True
• The angular frequency in SHM is measured in radians per second.


  True
• The velocity of an object in SHM is given by v = $- \omega A \sin(\omega t + \phi)$.
• SHM equations can be used to calculate the displacement, velocity, acceleration, period, and frequency of an object in motion.


  True
• At which point does the velocity in SHM reach its maximum?

  Midpoint of displacement
• What is the relationship between the amplitude and the total energy in SHM?

  Amplitude is proportional to $\sqrt{energy}$