17.2 A2 Level

Energy in simple harmonic motion

7 flashcards to master this topic

Key Concept Flip

Describe the energy transformation that occurs during simple harmonic motion (SHM).

Answer Flip

In SHM, there is a continuous interchange between kinetic energy (KE) and potential energy (PE). At maximum displacement, all energy is PE; at equilibrium, all energy is KE.

Definition Flip

What form of energy does a mass-spring system have at its maximum displacement during SHM?

Answer Flip

At maximum displacement, all the energy is stored as potential energy (PE) in the spring, specifically elastic potential energy.

Definition Flip

State the equation for the total energy (E) of a system undergoing simple harmonic motion.

Answer Flip

The total energy of a system undergoing SHM is given by: E = (1/2) * m * ω² * A², where m is the mass, ω is the angular frequency, and A is the amplitude.

Key Concept Flip

How does the total energy of a SHM system change if the amplitude is doubled, assuming all other factors remain constant?

Answer Flip

If the amplitude (A) is doubled, the total energy (E) increases by a factor of four, since E is proportional to A². Thus, the new energy E' = 4E.

Calculation Flip

A mass-spring system undergoing SHM has a total energy of 4J and an angular frequency of 2 rad/s. If the mass is 0.5 kg, what is the amplitude of the motion?

Answer Flip

Using E = (1/2) * m * ω² * A², rearrange for A: A = √(2E / (mω²)). Substituting values: A = √(2 * 4 / (0.5 * 2²)) = √4 = 2 m.

Key Concept Flip

How is kinetic energy related to velocity during SHM?

Answer Flip

Kinetic energy (KE) is maximum at the equilibrium position where velocity is maximum, and minimum (zero) at the extreme positions where velocity is zero. KE = (1/2)mv²

Key Concept Flip

Explain how potential energy changes as an object moves from the equilibrium position to its maximum displacement in SHM.

Answer Flip

As an object moves from the equilibrium position to maximum displacement, its potential energy increases, while its kinetic energy decreases. At maximum displacement, all energy is potential energy.

Ready to test yourself?

Practice with MCQ questions to check your understanding of Energy in simple harmonic motion.

Take Quiz
17.1 Simple harmonic oscillations 17.3 Damped and forced oscillations, resonance