Energy of Simple Harmonic Oscillators - AP Physics 1
Card 1 of 30
Determine the amplitude if the total energy is $32$ J and $k = 8$ N/m.
Determine the amplitude if the total energy is $32$ J and $k = 8$ N/m.
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$A = 2$ m. Solving $32 = \frac{1}{2}(8)A^2$ gives $A = 2$ m.
$A = 2$ m. Solving $32 = \frac{1}{2}(8)A^2$ gives $A = 2$ m.
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What is the unit of potential energy in the SI system?
What is the unit of potential energy in the SI system?
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Joule (J). Energy is measured in joules in the SI system.
Joule (J). Energy is measured in joules in the SI system.
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What is the formula for the total mechanical energy in a simple harmonic oscillator?
What is the formula for the total mechanical energy in a simple harmonic oscillator?
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$E = \frac{1}{2} k A^2$. Total energy equals half the spring constant times amplitude squared.
$E = \frac{1}{2} k A^2$. Total energy equals half the spring constant times amplitude squared.
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State the expression for potential energy in a simple harmonic oscillator.
State the expression for potential energy in a simple harmonic oscillator.
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$PE = \frac{1}{2} k x^2$. Energy stored in spring proportional to displacement squared.
$PE = \frac{1}{2} k x^2$. Energy stored in spring proportional to displacement squared.
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Calculate the total energy if $k = 150$ N/m and $A = 0.3$ m.
Calculate the total energy if $k = 150$ N/m and $A = 0.3$ m.
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$E = 6.75$ J. Using $E = \frac{1}{2}(150)(0.3)^2 = 6.75$ J.
$E = 6.75$ J. Using $E = \frac{1}{2}(150)(0.3)^2 = 6.75$ J.
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Which type of energy is zero at the maximum displacement of a harmonic oscillator?
Which type of energy is zero at the maximum displacement of a harmonic oscillator?
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Kinetic energy. At maximum displacement, velocity is zero making KE zero.
Kinetic energy. At maximum displacement, velocity is zero making KE zero.
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What is the relationship between total energy, kinetic energy, and potential energy?
What is the relationship between total energy, kinetic energy, and potential energy?
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$E = KE + PE$. Conservation of energy states total equals sum of parts.
$E = KE + PE$. Conservation of energy states total equals sum of parts.
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Find the spring constant if $E = 18$ J and $A = 0.3$ m.
Find the spring constant if $E = 18$ J and $A = 0.3$ m.
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$k = 400$ N/m. Solving $18 = \frac{1}{2}k(0.3)^2$ gives $k = 400$ N/m.
$k = 400$ N/m. Solving $18 = \frac{1}{2}k(0.3)^2$ gives $k = 400$ N/m.
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Identify the variable $x$ in the potential energy formula of a harmonic oscillator.
Identify the variable $x$ in the potential energy formula of a harmonic oscillator.
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Displacement from equilibrium. Distance from the equilibrium position of the oscillator.
Displacement from equilibrium. Distance from the equilibrium position of the oscillator.
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What is the form of energy when the displacement of a harmonic oscillator is maximum?
What is the form of energy when the displacement of a harmonic oscillator is maximum?
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Potential energy. At maximum displacement, velocity is zero so only PE exists.
Potential energy. At maximum displacement, velocity is zero so only PE exists.
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What is the form of energy when the velocity of a harmonic oscillator is maximum?
What is the form of energy when the velocity of a harmonic oscillator is maximum?
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Kinetic energy. At equilibrium, displacement is zero so only KE exists.
Kinetic energy. At equilibrium, displacement is zero so only KE exists.
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If $E = 15$ J, $KE = 9$ J at a point, find the potential energy.
If $E = 15$ J, $KE = 9$ J at a point, find the potential energy.
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$PE = 6$ J. Energy conservation: $PE = E - KE = 15 - 9 = 6$ J.
$PE = 6$ J. Energy conservation: $PE = E - KE = 15 - 9 = 6$ J.
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Determine the factor by which energy increases if amplitude is tripled.
Determine the factor by which energy increases if amplitude is tripled.
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Energy increases by a factor of 9. Energy is proportional to $A^2$, so tripling A increases E by $3^2 = 9$.
Energy increases by a factor of 9. Energy is proportional to $A^2$, so tripling A increases E by $3^2 = 9$.
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Find the total mechanical energy if $k = 200$ N/m and $A = 0.5$ m.
Find the total mechanical energy if $k = 200$ N/m and $A = 0.5$ m.
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$E = 25$ J. Using $E = \frac{1}{2}kA^2 = \frac{1}{2}(200)(0.5)^2 = 25$ J.
$E = 25$ J. Using $E = \frac{1}{2}kA^2 = \frac{1}{2}(200)(0.5)^2 = 25$ J.
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State the expression for kinetic energy in a simple harmonic oscillator.
State the expression for kinetic energy in a simple harmonic oscillator.
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$KE = \frac{1}{2} m v^2$. Standard kinetic energy formula with mass and velocity.
$KE = \frac{1}{2} m v^2$. Standard kinetic energy formula with mass and velocity.
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What does the variable $A$ represent in the energy formula of a harmonic oscillator?
What does the variable $A$ represent in the energy formula of a harmonic oscillator?
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Amplitude. Maximum displacement from equilibrium position.
Amplitude. Maximum displacement from equilibrium position.
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What does the variable $k$ represent in the energy formula of a harmonic oscillator?
What does the variable $k$ represent in the energy formula of a harmonic oscillator?
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Spring constant. The proportionality constant relating force to displacement.
Spring constant. The proportionality constant relating force to displacement.
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What remains constant for a simple harmonic oscillator in the absence of non-conservative forces?
What remains constant for a simple harmonic oscillator in the absence of non-conservative forces?
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Total mechanical energy. Energy conservation applies when no energy is lost to friction.
Total mechanical energy. Energy conservation applies when no energy is lost to friction.
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Find the displacement if $k = 50$ N/m and $PE = 4$ J.
Find the displacement if $k = 50$ N/m and $PE = 4$ J.
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$x = 0.4$ m. Solving $4 = \frac{1}{2}(50)x^2$ gives $x = 0.4$ m.
$x = 0.4$ m. Solving $4 = \frac{1}{2}(50)x^2$ gives $x = 0.4$ m.
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Which type of energy is zero at the equilibrium position of a harmonic oscillator?
Which type of energy is zero at the equilibrium position of a harmonic oscillator?
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Potential energy. At equilibrium, displacement is zero making PE zero.
Potential energy. At equilibrium, displacement is zero making PE zero.
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If $E = 10$ J, $PE = 6$ J at a point, find the kinetic energy.
If $E = 10$ J, $PE = 6$ J at a point, find the kinetic energy.
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$KE = 4$ J. Energy conservation: $KE = E - PE = 10 - 6 = 4$ J.
$KE = 4$ J. Energy conservation: $KE = E - PE = 10 - 6 = 4$ J.
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Calculate the mass if $v = 4$ m/s and $KE = 32$ J.
Calculate the mass if $v = 4$ m/s and $KE = 32$ J.
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$m = 4$ kg. Solving $32 = \frac{1}{2}m(4)^2$ gives $m = 4$ kg.
$m = 4$ kg. Solving $32 = \frac{1}{2}m(4)^2$ gives $m = 4$ kg.
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Find the spring constant if the total energy is $50$ J and $A = 0.4$ m.
Find the spring constant if the total energy is $50$ J and $A = 0.4$ m.
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$k = 625$ N/m. Solving $50 = \frac{1}{2}k(0.4)^2$ gives $k = 625$ N/m.
$k = 625$ N/m. Solving $50 = \frac{1}{2}k(0.4)^2$ gives $k = 625$ N/m.
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Calculate the kinetic energy if $m = 2$ kg and $v = 3$ m/s.
Calculate the kinetic energy if $m = 2$ kg and $v = 3$ m/s.
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$KE = 9$ J. Using $KE = \frac{1}{2}mv^2 = \frac{1}{2}(2)(3)^2 = 9$ J.
$KE = 9$ J. Using $KE = \frac{1}{2}mv^2 = \frac{1}{2}(2)(3)^2 = 9$ J.
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If $m = 0.5$ kg and $v = 5$ m/s, calculate the kinetic energy.
If $m = 0.5$ kg and $v = 5$ m/s, calculate the kinetic energy.
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$KE = 6.25$ J. Using $KE = \frac{1}{2}(0.5)(5)^2 = 6.25$ J.
$KE = 6.25$ J. Using $KE = \frac{1}{2}(0.5)(5)^2 = 6.25$ J.
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Find $v$ if $KE = 18$ J and $m = 3$ kg.
Find $v$ if $KE = 18$ J and $m = 3$ kg.
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$v = 4$ m/s. Solving $18 = \frac{1}{2}(3)v^2$ gives $v = 4$ m/s.
$v = 4$ m/s. Solving $18 = \frac{1}{2}(3)v^2$ gives $v = 4$ m/s.
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What happens to the total energy if the amplitude is doubled in a harmonic oscillator?
What happens to the total energy if the amplitude is doubled in a harmonic oscillator?
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Total energy quadruples. Energy is proportional to $A^2$, so doubling A increases E by $2^2 = 4$.
Total energy quadruples. Energy is proportional to $A^2$, so doubling A increases E by $2^2 = 4$.
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If $m = 1.5$ kg and $v = 2$ m/s, find the kinetic energy.
If $m = 1.5$ kg and $v = 2$ m/s, find the kinetic energy.
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$KE = 3$ J. Using $KE = \frac{1}{2}(1.5)(2)^2 = 3$ J.
$KE = 3$ J. Using $KE = \frac{1}{2}(1.5)(2)^2 = 3$ J.
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Determine the energy type at maximum speed in a harmonic oscillator.
Determine the energy type at maximum speed in a harmonic oscillator.
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Kinetic energy. Maximum speed occurs at equilibrium where all energy is kinetic.
Kinetic energy. Maximum speed occurs at equilibrium where all energy is kinetic.
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What is the unit of amplitude in the SI system?
What is the unit of amplitude in the SI system?
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Meter (m). Distance is measured in meters in the SI system.
Meter (m). Distance is measured in meters in the SI system.
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