7.4 Energy of Simple Harmonic Oscillators

• Simple harmonic motion (SHM) results in a periodic, sinusoidal motion due to a restoring force proportional to displacement
• What is the total mechanical energy of a simple harmonic oscillator equal to?

  Kinetic + potential energy
• At what position is potential energy maximum in SHM?

  Amplitude
• Match the variables in the total mechanical energy equation with their definitions:

  k ↔️ Spring constant

  A ↔️ Amplitude

  ω ↔️ Angular frequency
• What is the acceleration of an object in SHM at its equilibrium position?

  Zero
• Where is potential energy maximum in a mass-spring system undergoing SHM?

  Amplitude
• At which position is the kinetic energy of a mass-spring system in SHM maximum?

  Equilibrium
• Match the position of a mass-spring system in SHM with its energy values:

  Equilibrium ↔️ Kinetic energy is maximum

  Amplitude ↔️ Potential energy is maximum

  Intermediate ↔️ Kinetic and potential energy are positive
• What is the formula for potential energy in SHM?

  U = \frac{1}{2}kx^{2}</latex>
• Match the type of motion with its characteristics:

  Simple Harmonic ↔️ Restoring force proportional to displacement

  Uniform Circular ↔️ Centripetal acceleration

  Constant Acceleration ↔️ Constant force
• Potential energy is maximum at the amplitude in SHM.


  True
• Potential energy in SHM is zero at the equilibrium position.


  True
• Potential energy in SHM is maximum at the equilibrium position.

  False
• Velocity in SHM varies sinusoidally with displacement.


  True
• What is the maximum kinetic energy in SHM in terms of mass *m*, angular frequency *ω*, and amplitude *A*?

  K_\text{\max} =$\frac{1}{2}m\omega^{2}A^{2}$
• What are the values of kinetic and potential energy at the amplitude in SHM?

  Zero and maximum
• At what position does an object in SHM experience zero acceleration?

  Equilibrium position
• The total mechanical energy of a simple harmonic oscillator is given by the equation $E_\text{total} =$$E_\text{kinetic} +$$E_\text{potential}$.


  True
• The total mechanical energy of a simple harmonic oscillator remains constant if there are no dissipative forces.

  True
• In SHM, the object experiences zero restoring force at its equilibrium position.


  True
• What is the total mechanical energy of a simple harmonic oscillator (SHO)?

  Kinetic + potential energy
• The total mechanical energy in SHM can be expressed as $E_\text{total} =$$\frac{1}{2}kA^{2}$


  True
• Arrange the following in order of decreasing potential energy in SHM:

  1️⃣ Amplitude

  2️⃣ Intermediate

  3️⃣ Equilibrium
• The potential energy in SHM is proportional to the square of the displacement.
• In a simple harmonic oscillator, kinetic energy is maximum at the equilibrium position.
• What is the total energy of a simple harmonic oscillator in terms of *k* and *A*?

  $\frac{1}{2}kA^{2}$
• In the potential energy formula, *k* is the spring constant.
• Where is kinetic energy maximum in SHM?

  Equilibrium
• What is the formula for velocity in SHM in terms of angular frequency *ω* and amplitude *A*?

  $v =$$\omega A \cos(\omega t)$
• During SHM, energy is continuously transformed between kinetic and potential energy.

  True
• Total mechanical energy remains constant in ideal SHM due to no dissipative forces.


  True
• In SHM, the restoring force is proportional to displacement and the acceleration is zero at equilibrium.


  True
• In SHM, kinetic energy is maximum at the equilibrium
• What is the equation for the total mechanical energy in SHM involving amplitude, angular frequency, and mass?

  $E_\text{total} =$$\frac{1}{2}kA^{2}$
• The total mechanical energy in SHM is determined by the amplitude and angular frequency
• For a mass-spring system in SHM, kinetic energy is maximum at the equilibrium position.
• The total mechanical energy in SHM remains constant throughout the oscillation.
• In the formula for total mechanical energy, *ω* represents the angular frequency.
• Kinetic energy in SHM is maximum at the amplitude.

  False
• What is the restoring force in simple harmonic motion (SHM) proportional to?

  Displacement