Why does the total energy of an ideal system in SHM stay constant ?

It is assumed that no work is done by resistive forces such as drag or friction, so no energy enters or leaves the system.

Which potential energy changes in a horizontal object-spring system?

Only the elastic potential energy of the spring, as the gravitational potential energy is unchanged.

Why must the Earth be included in a vertical object-spring system?

The gravitational potential energy changes as well as the elastic potential energy, and the Earth provides the field in which it varies.

How must elastic potential energy be defined in a vertical object-spring-Earth system?

It must be defined using the displacement from the spring's natural length .

In a vertical object-spring-Earth system, h = 0 for gravitational potential energy can be set at .......... and the total energy remains constant.

In a vertical object-spring-Earth system, h = 0 for gravitational potential energy can be set at any point and the total energy remains constant.

True or False? A system in SHM at maximum displacement has zero total energy.

False. Kinetic energy is zero there, but potential energy is at its maximum . The total energy is constant throughout.

State the energies at the equilibrium position in SHM.

Kinetic energy: maximum, equal to the total energy Potential energy: zero

State the energies at the amplitude positions in SHM.

Kinetic energy: zero Potential energy: maximum, equal to the total energy

Why is kinetic energy a maximum at equilibrium whichever direction the object is moving?

Kinetic energy is proportional to velocity squared , so squaring a negative velocity gives the same positive maximum value.

How does increasing the amplitude affect the total energy of an SHM system?

The total energy increases . More work is done to displace the object to a larger amplitude, so the maximum potential energy is greater.

In SHM, potential energy increases as the object moves .......... the restoring force.

In SHM, potential energy increases as the object moves against the restoring force.

AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 7: OscillationsEnergy of Simple Harmonic Oscillators

Energy of Simple Harmonic Oscillators (College Board AP® Physics 1: Algebra-Based): Flashcards

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FrontTotal Energy of SHM
State the equation for the total energy of a system in SHM.
BackTotal Energy of SHM
$E_{total} = U + K$
$E_{total}$ = total energy of the system (J)
$U$ = total potential energy (J)
$K$ = total kinetic energy (J)
BackTotal Energy of SHM
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Cards in this collection (15)

State the equation for the total energy of a system in SHM.
$E_{total} = U + K$
- $E_{total}$ = total energy of the system (J)
- $U$ = total potential energy (J)
- $K$ = total kinetic energy (J)
Why does the total energy of an ideal system in SHM stay constant?
It is assumed that no work is done by resistive forces such as drag or friction, so no energy enters or leaves the system.
Which potential energy changes in a horizontal object-spring system?
Only the elastic potential energy of the spring, as the gravitational potential energy is unchanged.
Why must the Earth be included in a vertical object-spring system?
The gravitational potential energy changes as well as the elastic potential energy, and the Earth provides the field in which it varies.
How must elastic potential energy be defined in a vertical object-spring-Earth system?
It must be defined using the displacement from the spring's natural length.
In a vertical object-spring-Earth system, h = 0 for gravitational potential energy can be set at .......... and the total energy remains constant.
In a vertical object-spring-Earth system, h = 0 for gravitational potential energy can be set at any point and the total energy remains constant.
True or False?
A system in SHM at maximum displacement has zero total energy.
False.
Kinetic energy is zero there, but potential energy is at its maximum. The total energy is constant throughout.
State the energies at the equilibrium position in SHM.
- Kinetic energy: maximum, equal to the total energy
- Potential energy: zero
State the energies at the amplitude positions in SHM.
- Kinetic energy: zero
- Potential energy: maximum, equal to the total energy
Why is kinetic energy a maximum at equilibrium whichever direction the object is moving?
Kinetic energy is proportional to velocity squared, so squaring a negative velocity gives the same positive maximum value.
State the equation for the elastic potential energy stored in a spring.
$U_{s} = \frac{1}{2} k {(∆ x)}^{2}$
- $U_{s}$ = elastic potential energy (J)
- $k$ = spring constant (N/m)
- $∆ x$ = displacement (m)
State the equation for the total energy of an object-ideal spring system.
$E_{total} = \frac{1}{2} k A^{2}$
- $E_{total}$ = total energy (J)
- $k$ = spring constant (N/m)
- $A$ = amplitude (m)
How does increasing the amplitude affect the total energy of an SHM system?
The total energy increases. More work is done to displace the object to a larger amplitude, so the maximum potential energy is greater.
In SHM, potential energy increases as the object moves .......... the restoring force.
In SHM, potential energy increases as the object moves against the restoring force.
True or False?
Doubling the amplitude of an object-ideal spring system doubles its total energy.
False.
Total energy is proportional to amplitude squared ( $E_{total} = \frac{1}{2} k A^{2}$ ), so doubling the amplitude makes the total energy four times larger.

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