7.4 Energy in Simple Harmonic Motion

• At the equilibrium position in SHM, kinetic energy is maximum and potential energy is zero.


  True
• Arrange the energy distribution in SHM based on position:

  1️⃣ Equilibrium: Kinetic energy is maximum, potential energy is minimum

  2️⃣ Maximum Displacement: Kinetic energy is minimum, potential energy is maximum

  3️⃣ Between Equilibrium and Max. Displacement: Both kinetic and potential energy vary
• What is the formula for potential energy in SHM?

  U = \frac{1}{2}kx^{2}</latex>
• The total mechanical energy in SHM can be expressed as the sum of kinetic and potential energy, which equals $E =$$\frac{1}{2}mv^{2} +$$\frac{1}{2}kx^{2}$
• In the kinetic energy equation, `v` represents the object's velocity
• What does `x` represent in the potential energy equation?

  Displacement from equilibrium
• The total mechanical energy in SHM is the sum of kinetic and potential energy.

  True
• At the equilibrium position, kinetic energy is maximum and potential energy is minimum.


  True
• The total energy in SHM oscillates between kinetic and potential energy while remaining constant
• In SHM, the restoring force is proportional to the displacement.

  True
• At which position is kinetic energy maximum in SHM?

  Equilibrium
• What does `m` represent in the kinetic energy equation in SHM?

  Mass of the object
• In the potential energy equation, `k` is also known as the spring
• In SHM, the restoring force is proportional to the displacement
• What is the equation for kinetic energy in SHM?

  K = \frac{1}{2}mv^{2}</latex>
• Match the variable with its definition in the potential energy equation:

  k ↔️ Spring constant

  x ↔️ Displacement from equilibrium

  U ↔️ Potential energy
• What is the equation for the total mechanical energy in SHM?

  $E =$$\frac{1}{2}mv^{2} +$$\frac{1}{2}kx^{2}$
• Arrange the positions in SHM based on the transformation of energy:

  1️⃣ Equilibrium: Kinetic energy is maximum, potential energy is minimum

  2️⃣ Maximum displacement: Kinetic energy is minimum, potential energy is maximum

  3️⃣ Between equilibrium and maximum displacement: Kinetic and potential energy vary
• Match the position in SHM with the energy distribution:

  Equilibrium ↔️ Maximum kinetic, minimum potential

  Maximum displacement ↔️ Minimum kinetic, maximum potential

  Between ↔️ Varies
• Why does the total energy in SHM remain constant?

  Continuous transformation of energy
• Higher frequency in SHM means more oscillations per unit time
• Match the quantity in SHM with its relationship to the system:

  Amplitude ↔️ Maximum displacement

  Frequency ↔️ Oscillations per unit time

  Energy ↔️ Constant, oscillates between forms
• What is simple harmonic motion (SHM)?

  Periodic motion with restoring force proportional to displacement
• At the maximum displacement in SHM, kinetic energy is zero, and potential energy is at its maximum
• Match the type of motion with its restoring force and displacement:

  Simple Harmonic ↔️ Proportional to displacement, linear

  Uniform Circular ↔️ Centripetal (towards center), circular

  Free Fall ↔️ Gravitational (constant), parabolic
• What is the formula for kinetic energy in SHM?

  $K =$$\frac{1}{2}mv^{2}$
• The total mechanical energy in SHM remains constant throughout the oscillation.


  True
• What is the equation for kinetic energy in SHM?

  $K =$$\frac{1}{2}mv^{2}$
• The spring constant `k` in the potential energy equation is a measure of the force required to displace the object from equilibrium.


  True
• The total energy of the system in SHM remains constant
• What is the equation for total mechanical energy in SHM?

  E = \frac{1}{2}mv^{2} + \frac{1}{2}kx^{2}</latex>
• Match the position with the energy state:

  Equilibrium ↔️ Kinetic energy maximum

  Maximum Displacement ↔️ Potential energy maximum
• What is the defining characteristic of SHM in terms of restoring force and displacement?

  Proportional to displacement
• Match the motion type with its restoring force:

  Simple Harmonic ↔️ Proportional to displacement

  Uniform Circular ↔️ Centripetal

  Free Fall ↔️ Gravitational
• Potential energy in SHM is at its maximum when the object reaches its maximum displacement
• The potential energy in SHM is derived from the work done against the restoring force.


  True
• The total energy in simple harmonic motion remains constant.

  True
• In SHM, the potential energy is given by $U =$$\frac{1}{2}kx^{2}$
• In SHM, kinetic energy and potential energy continuously exchange forms.


  True
• At the equilibrium position in SHM, kinetic energy is maximum, and potential energy is minimum