7.8. Energy in Free Vibration

Try these first

1. 1.

   Define kinetic energy in the context of free vibration.

   Hint

   Remember the relationship between mass and velocity in your definition.

2. 2.

   What is the formula for potential energy in a mass-spring system?

   Hint

   Think about the spring constant and how displacement affects energy.

3. 3.

   What is the formula for kinetic energy in a mass-spring system?

   • KE = mgh
   • KE = 1/2 mv²
   • KE = 1/2 kx²

   Hint

   Which one of these formulas relates to motion?

4. 4.

   True or False: Potential energy in a mass-spring system is maximum at equilibrium.

   • True
   • False

   Hint

   Think about where the spring is compressed or stretched the most.

5. 5.

   A mass-spring system oscillates with a mass of 10 kg and a spring constant of 400 N/m. Calculate the total mechanical energy when the displacement is 0.4 m.

   Hint

   Calculate PE first and remember energy is conserved.

6. 6.

   Consider a system where the kinetic energy at the equilibrium position is 50 Joules. If the maximum displacement occurs where potential energy is 70 Joules, calculate the total energy of the system.

   Hint

   Total energy is the sum of both forms at any point in the oscillation.