7.3 Representing and Analyzing SHM

• In SHM, the restoring force is independent of displacement.

  False
• SHM is characterized by sinusoidal graphs of displacement, velocity, and acceleration over time.


  True
• The angular frequency in SHM represents the rate of change of the angle
• Match the parameters in SHM and linear motion with their physical meanings:

  Amplitude (A) ↔️ Maximum displacement

  Angular Frequency (ω) ↔️ Rate of change of angle

  Velocity (v) ↔️ Rate of change of position

  Initial Position (x_0) ↔️ Position at t = 0
• Arrange the following aspects to compare SHM and linear motion:

  1️⃣ Function: $x(t) =$$A \cos(\omega t + \phi)$ vs $x(t) =$$vt +$$x_{0}$

  2️⃣ Curve: Sinusoidal vs Linear

  3️⃣ Parameters: Amplitude, Angular Frequency vs Velocity, Initial Position
• The displacement graph in SHM is sinusoidal, unlike linear motion which has a linear or parabolic graph.


  True
• Arrange the following types of graphs in order from SHM displacement to SHM velocity to SHM acceleration.

  1️⃣ Sinusoidal (Displacement)

  2️⃣ Sinusoidal (Velocity)

  3️⃣ Sinusoidal (Acceleration)
• The velocity in linear motion changes linearly with time if acceleration is constant.


  True
• In the displacement function of SHM, 'A' represents the amplitude
• What is Simple Harmonic Motion (SHM)?

  Periodic motion with restoring force proportional to displacement
• What type of motion does a mass-spring system exhibit when the restoring force is proportional to the mass's displacement?

  Simple Harmonic Motion
• What does the amplitude 'A' represent in the displacement function of SHM?

  Maximum displacement from equilibrium
• The phase constant in SHM determines the initial angle at time t = 0.

  True
• The amplitude in the displacement function of SHM represents the maximum displacement from the equilibrium position.
• What does 'A' represent in the displacement function of SHM?

  Amplitude
• What is the angular frequency denoted by in the SHM displacement function?

  $\omega$
• What is the phase difference between the velocity and displacement functions in SHM?

  $\pi / 2$
• The acceleration in SHM is proportional to the displacement and opposite in sign.
• What is the velocity function in linear motion with constant acceleration?

  $v(t) =$$u +$$at$
• What does 'A' represent in the velocity function of SHM?

  Amplitude
• What is the velocity function in SHM?

  $v(t) =$$- A \omega \sin(\omega t + \phi)$
• In a mass-spring system, where does the velocity of the mass peak?

  Equilibrium position
• Unlike linear motion, the acceleration in SHM varies sinusoidally
• Match the function with its description in SHM:

  Displacement ↔️ $x(t) =$$A \cos(\omega t + \phi)$

  Velocity ↔️ $v(t) =$$- A \omega \sin(\omega t + \phi)$

  Acceleration ↔️ $a(t) =$$- A \omega^{2} \cos(\omega t + \phi)$
• In SHM, the kinetic energy is maximum when the velocity is at its peak
• What is the formula for the total energy in SHM?

  $E_{\text{total}} =$$\frac{1}{2}mA^{2}\omega^{2}$
• The total energy in SHM remains constant
• The maximum displacement from equilibrium in SHM is called the amplitude
• Simple Harmonic Motion is characterized by sinusoidal graphs of displacement, velocity, and acceleration over time.
• What is the general formula for the displacement function in SHM?

  $x(t) =$$A \cos(\omega t + \phi)$
• The velocity function in SHM produces a sinusoidal graph.
• In SHM, the acceleration function is directly proportional to and opposite in sign to the displacement function.


  True
• The angular frequency in SHM is represented by the symbol ω
• The velocity in SHM is maximum at the equilibrium position.

  True
• Unlike constant linear velocity, the velocity in SHM varies sinusoidally
• The velocity curve in SHM is sinusoidal
• What is the acceleration function in SHM?

  $a(t) =$$- A \omega^{2} \cos(\omega t + \phi)$
• What type of graph does the acceleration in SHM produce?

  Sinusoidal
• What is the displacement function in SHM?

  $x(t) =$$A \cos(\omega t + \phi)$
• What is the potential energy function in SHM?

  $U =$$\frac{1}{2}kA^{2}\cos^{2}(\omega t + \phi)$