7.4 Energy in Simple Harmonic Motion

• What type of motion is simple harmonic motion (SHM)?

  Periodic motion
• In SHM, the restoring force is proportional to the object's displacement
• SHM repeats at regular intervals, making it periodic.
• What is the formula for potential energy in SHM?

  $U =$$\frac{1}{2}kx^{2}$
• The potential energy in SHM is maximum at the maximum displacement
• Match the position with the potential energy in SHM:

  Equilibrium ↔️ Minimum potential energy

  Maximum displacement ↔️ Maximum potential energy
• What is the formula for kinetic energy in SHM?

  $K =$$\frac{1}{2}mv^{2}$
• Kinetic energy in SHM is maximum at the equilibrium position.
• Arrange the key features of SHM in a logical order:

  1️⃣ Restoring Force proportional to displacement

  2️⃣ Proportionality: \(F = -kx\)

  3️⃣ Periodicity: Motion repeats

  4️⃣ Equilibrium Point: Net force is zero
• What is the relationship between the restoring force and the displacement in SHM?

  Directly proportional
• The restoring force in SHM is proportional to the displacement from equilibrium.
• The proportionality constant in the restoring force equation is called the spring constant.
• What is a key feature of SHM that describes the repetition of motion at regular intervals?

  Periodicity
• The equilibrium point in SHM is where the net force is zero.
• Match the feature of SHM with its description:

  Restoring Force ↔️ Proportional to displacement

  Periodicity ↔️ Motion repeats at regular intervals

  Equilibrium Point ↔️ Net force is zero
• The potential energy in SHM is given by the formula U = \frac{1}{2}kx^{2}.
• What does \(k\) represent in the potential energy formula of SHM?

  Spring constant
• The potential energy in SHM is maximum at the equilibrium position.

  False
• The kinetic energy in SHM is given by the formula K = \frac{1}{2}mv^{2}.
• Where is the kinetic energy in SHM maximum?

  Equilibrium position
• The total mechanical energy in SHM remains constant if no dissipative forces are present.
• The total mechanical energy in SHM is the sum of kinetic and potential energy.
• Arrange the energy types in SHM based on their values at different positions:

  1️⃣ Kinetic energy is maximum at equilibrium

  2️⃣ Potential energy is minimum at equilibrium

  3️⃣ Total mechanical energy remains constant
• What type of forces, if present, can cause the total mechanical energy in SHM to decrease?

  Non-conservative forces
• Energy conservation in SHM holds only if there are no non-conservative forces acting.
• The total energy in SHM can also be expressed as \(E = \frac{1}{2}kA^{2}\), where \(A\) is the amplitude.