AP Physics 1 Flashcards: Energy Of Simple Harmonic Oscillators

What this deck covers

This deck focuses on Energy Of Simple Harmonic Oscillators, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 1.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the unit of potential energy in the SI system?

Answer: Joule (J). Energy is measured in joules in the SI system.

Flashcard 2: Determine the factor by which energy increases if amplitude is tripled.

Answer: Energy increases by a factor of 9. Energy is proportional to $A^2$, so tripling A increases E by $3^2 = 9$.

Flashcard 3: Which type of energy is zero at the maximum displacement of a harmonic oscillator?

Answer: Kinetic energy. At maximum displacement, velocity is zero making KE zero.

Flashcard 4: What is the relationship between total energy, kinetic energy, and potential energy?

Answer: $E = KE + PE$. Conservation of energy states total equals sum of parts.

Flashcard 5: What is the form of energy when the displacement of a harmonic oscillator is maximum?

Answer: Potential energy. At maximum displacement, velocity is zero so only PE exists.

Flashcard 6: What is the unit of amplitude in the SI system?

Answer: Meter (m). Distance is measured in meters in the SI system.

Flashcard 7: What is the unit of displacement in the SI system?

Answer: Meter (m). Distance is measured in meters in the SI system.

Flashcard 8: Determine the energy type at maximum speed in a harmonic oscillator.

Answer: Kinetic energy. Maximum speed occurs at equilibrium where all energy is kinetic.

Flashcard 9: Calculate the total energy if $k = 150$ N/m and $A = 0.3$ m.

Answer: $E = 6.75$ J. Using $E = \frac{1}{2}(150)(0.3)^2 = 6.75$ J.

Flashcard 10: What happens to the total energy if the amplitude is doubled in a harmonic oscillator?

Answer: Total energy quadruples. Energy is proportional to $A^2$, so doubling A increases E by $2^2 = 4$.

Flashcard 11: Calculate the kinetic energy if $m = 2$ kg and $v = 3$ m/s.

Answer: $KE = 9$ J. Using $KE = \frac{1}{2}mv^2 = \frac{1}{2}(2)(3)^2 = 9$ J.

Flashcard 12: Find the displacement if $k = 50$ N/m and $PE = 4$ J.

Answer: $x = 0.4$ m. Solving $4 = \frac{1}{2}(50)x^2$ gives $x = 0.4$ m.

Flashcard 13: Which type of energy is zero at the maximum displacement of a harmonic oscillator?

Answer: Kinetic energy. At maximum displacement, velocity is zero making KE zero.

Flashcard 14: If $E = 10$ J, $PE = 6$ J at a point, find the kinetic energy.

Answer: $KE = 4$ J. Energy conservation: $KE = E - PE = 10 - 6 = 4$ J.

Flashcard 15: State the expression for potential energy in a simple harmonic oscillator.

Answer: $PE = \frac{1}{2} k x^2$. Energy stored in spring proportional to displacement squared.

Flashcard 16: What does the variable $A$ represent in the energy formula of a harmonic oscillator?

Answer: Amplitude. Maximum displacement from equilibrium position.

Flashcard 17: State the expression for kinetic energy in a simple harmonic oscillator.

Answer: $KE = \frac{1}{2} m v^2$. Standard kinetic energy formula with mass and velocity.

Flashcard 18: If $m = 1.5$ kg and $v = 2$ m/s, find the kinetic energy.

Answer: $KE = 3$ J. Using $KE = \frac{1}{2}(1.5)(2)^2 = 3$ J.

Flashcard 19: What is the relationship between total energy, kinetic energy, and potential energy?

Answer: $E = KE + PE$. Conservation of energy states total equals sum of parts.

Flashcard 20: What is the unit of kinetic energy in the SI system?

Answer: Joule (J). Energy is measured in joules in the SI system.

Flashcard 21: Find the spring constant if $E = 18$ J and $A = 0.3$ m.

Answer: $k = 400$ N/m. Solving $18 = \frac{1}{2}k(0.3)^2$ gives $k = 400$ N/m.

Flashcard 22: Calculate the kinetic energy if $m = 2$ kg and $v = 3$ m/s.

Answer: $KE = 9$ J. Using $KE = \frac{1}{2}mv^2 = \frac{1}{2}(2)(3)^2 = 9$ J.

Flashcard 23: What is the formula for the total mechanical energy in a simple harmonic oscillator?

Answer: $E = \frac{1}{2} k A^2$. Total energy equals half the spring constant times amplitude squared.

Flashcard 24: What is the unit of displacement in the SI system?

Answer: Meter (m). Distance is measured in meters in the SI system.

Flashcard 25: What is the unit of total mechanical energy in the SI system?

Answer: Joule (J). Energy is measured in joules in the SI system.

Flashcard 26: Find the total mechanical energy if $k = 200$ N/m and $A = 0.5$ m.

Answer: $E = 25$ J. Using $E = \frac{1}{2}kA^2 = \frac{1}{2}(200)(0.5)^2 = 25$ J.

Flashcard 27: If $E = 15$ J, $KE = 9$ J at a point, find the potential energy.

Answer: $PE = 6$ J. Energy conservation: $PE = E - KE = 15 - 9 = 6$ J.

Flashcard 28: What is the unit of the spring constant $k$ in the SI system?

Answer: Newton per meter (N/m). Force per unit displacement has units of N/m.

Flashcard 29: What is the unit of kinetic energy in the SI system?

Answer: Joule (J). Energy is measured in joules in the SI system.

Flashcard 30: What remains constant for a simple harmonic oscillator in the absence of non-conservative forces?

Answer: Total mechanical energy. Energy conservation applies when no energy is lost to friction.

Flashcard 31: Find the total mechanical energy if $k = 200$ N/m and $A = 0.5$ m.

Answer: $E = 25$ J. Using $E = \frac{1}{2}kA^2 = \frac{1}{2}(200)(0.5)^2 = 25$ J.

Flashcard 32: If $E = 15$ J, $KE = 9$ J at a point, find the potential energy.

Answer: $PE = 6$ J. Energy conservation: $PE = E - KE = 15 - 9 = 6$ J.

Flashcard 33: If $k = 250$ N/m and $A = 0.1$ m, calculate the total energy.

Answer: $E = 1.25$ J. Using $E = \frac{1}{2}(250)(0.1)^2 = 1.25$ J.

Flashcard 34: State the expression for potential energy in a simple harmonic oscillator.

Answer: $PE = \frac{1}{2} k x^2$. Energy stored in spring proportional to displacement squared.

Flashcard 35: Find the spring constant if the total energy is $50$ J and $A = 0.4$ m.

Answer: $k = 625$ N/m. Solving $50 = \frac{1}{2}k(0.4)^2$ gives $k = 625$ N/m.

Flashcard 36: Which type of energy is zero at the equilibrium position of a harmonic oscillator?

Answer: Potential energy. At equilibrium, displacement is zero making PE zero.

Flashcard 37: What does the variable $k$ represent in the energy formula of a harmonic oscillator?

Answer: Spring constant. The proportionality constant relating force to displacement.

Flashcard 38: Find the spring constant if the total energy is $50$ J and $A = 0.4$ m.

Answer: $k = 625$ N/m. Solving $50 = \frac{1}{2}k(0.4)^2$ gives $k = 625$ N/m.

Flashcard 39: Identify the variable $x$ in the potential energy formula of a harmonic oscillator.

Answer: Displacement from equilibrium. Distance from the equilibrium position of the oscillator.

Flashcard 40: Determine the amplitude if the total energy is $32$ J and $k = 8$ N/m.

Answer: $A = 2$ m. Solving $32 = \frac{1}{2}(8)A^2$ gives $A = 2$ m.

Flashcard 41: If $k = 250$ N/m and $A = 0.1$ m, calculate the total energy.

Answer: $E = 1.25$ J. Using $E = \frac{1}{2}(250)(0.1)^2 = 1.25$ J.

Flashcard 42: What does the variable $k$ represent in the energy formula of a harmonic oscillator?

Answer: Spring constant. The proportionality constant relating force to displacement.

Flashcard 43: If $E = 10$ J, $PE = 6$ J at a point, find the kinetic energy.

Answer: $KE = 4$ J. Energy conservation: $KE = E - PE = 10 - 6 = 4$ J.

Flashcard 44: Find $x$ if $PE = 5$ J and $k = 125$ N/m.

Answer: $x = 0.2$ m. Solving $5 = \frac{1}{2}(125)x^2$ gives $x = 0.2$ m.

Flashcard 45: Identify the variable $x$ in the potential energy formula of a harmonic oscillator.

Answer: Displacement from equilibrium. Distance from the equilibrium position of the oscillator.

Flashcard 46: Find $v$ if $KE = 18$ J and $m = 3$ kg.

Answer: $v = 4$ m/s. Solving $18 = \frac{1}{2}(3)v^2$ gives $v = 4$ m/s.

Flashcard 47: If $m = 0.5$ kg and $v = 5$ m/s, calculate the kinetic energy.

Answer: $KE = 6.25$ J. Using $KE = \frac{1}{2}(0.5)(5)^2 = 6.25$ J.

Flashcard 48: What is the form of energy when the displacement of a harmonic oscillator is maximum?

Answer: Potential energy. At maximum displacement, velocity is zero so only PE exists.

Flashcard 49: Find the spring constant if $E = 18$ J and $A = 0.3$ m.

Answer: $k = 400$ N/m. Solving $18 = \frac{1}{2}k(0.3)^2$ gives $k = 400$ N/m.

Flashcard 50: What is the unit of the spring constant $k$ in the SI system?

Answer: Newton per meter (N/m). Force per unit displacement has units of N/m.

Flashcard 51: What is the unit of amplitude in the SI system?

Answer: Meter (m). Distance is measured in meters in the SI system.

Flashcard 52: Find $v$ if $KE = 18$ J and $m = 3$ kg.

Answer: $v = 4$ m/s. Solving $18 = \frac{1}{2}(3)v^2$ gives $v = 4$ m/s.

Flashcard 53: What is the form of energy when the velocity of a harmonic oscillator is maximum?

Answer: Kinetic energy. At equilibrium, displacement is zero so only KE exists.

Flashcard 54: If $m = 1.5$ kg and $v = 2$ m/s, find the kinetic energy.

Answer: $KE = 3$ J. Using $KE = \frac{1}{2}(1.5)(2)^2 = 3$ J.

Flashcard 55: Calculate the total energy if $k = 150$ N/m and $A = 0.3$ m.

Answer: $E = 6.75$ J. Using $E = \frac{1}{2}(150)(0.3)^2 = 6.75$ J.

Flashcard 56: Determine the factor by which energy increases if amplitude is tripled.

Answer: Energy increases by a factor of 9. Energy is proportional to $A^2$, so tripling A increases E by $3^2 = 9$.

Flashcard 57: Which type of energy is zero at the equilibrium position of a harmonic oscillator?

Answer: Potential energy. At equilibrium, displacement is zero making PE zero.

Flashcard 58: Calculate the mass if $v = 4$ m/s and $KE = 32$ J.

Answer: $m = 4$ kg. Solving $32 = \frac{1}{2}m(4)^2$ gives $m = 4$ kg.

Flashcard 59: Calculate the potential energy if $k = 100$ N/m and $x = 0.1$ m.

Answer: $PE = 0.5$ J. Using $PE = \frac{1}{2}kx^2 = \frac{1}{2}(100)(0.1)^2 = 0.5$ J.

Flashcard 60: State the expression for kinetic energy in a simple harmonic oscillator.

Answer: $KE = \frac{1}{2} m v^2$. Standard kinetic energy formula with mass and velocity.

Flashcard 61: Determine the energy type at maximum speed in a harmonic oscillator.

Answer: Kinetic energy. Maximum speed occurs at equilibrium where all energy is kinetic.

Flashcard 62: What is the form of energy when the velocity of a harmonic oscillator is maximum?

Answer: Kinetic energy. At equilibrium, displacement is zero so only KE exists.

Flashcard 63: Find the displacement if $k = 50$ N/m and $PE = 4$ J.

Answer: $x = 0.4$ m. Solving $4 = \frac{1}{2}(50)x^2$ gives $x = 0.4$ m.

Flashcard 64: If $k = 200$ N/m and $x = 0.2$ m, find the potential energy.

Answer: $PE = 4$ J. Using $PE = \frac{1}{2}(200)(0.2)^2 = 4$ J.

Flashcard 65: Determine the amplitude if the total energy is $32$ J and $k = 8$ N/m.

Answer: $A = 2$ m. Solving $32 = \frac{1}{2}(8)A^2$ gives $A = 2$ m.

Flashcard 66: Find $x$ if $PE = 5$ J and $k = 125$ N/m.

Answer: $x = 0.2$ m. Solving $5 = \frac{1}{2}(125)x^2$ gives $x = 0.2$ m.

Flashcard 67: What is the formula for the total mechanical energy in a simple harmonic oscillator?

Answer: $E = \frac{1}{2} k A^2$. Total energy equals half the spring constant times amplitude squared.

Flashcard 68: If $m = 0.5$ kg and $v = 5$ m/s, calculate the kinetic energy.

Answer: $KE = 6.25$ J. Using $KE = \frac{1}{2}(0.5)(5)^2 = 6.25$ J.

Flashcard 69: What does the variable $A$ represent in the energy formula of a harmonic oscillator?

Answer: Amplitude. Maximum displacement from equilibrium position.

Flashcard 70: Calculate the potential energy if $k = 100$ N/m and $x = 0.1$ m.

Answer: $PE = 0.5$ J. Using $PE = \frac{1}{2}kx^2 = \frac{1}{2}(100)(0.1)^2 = 0.5$ J.

Flashcard 71: What remains constant for a simple harmonic oscillator in the absence of non-conservative forces?

Answer: Total mechanical energy. Energy conservation applies when no energy is lost to friction.

Flashcard 72: If $k = 200$ N/m and $x = 0.2$ m, find the potential energy.

Answer: $PE = 4$ J. Using $PE = \frac{1}{2}(200)(0.2)^2 = 4$ J.

Flashcard 73: What happens to the total energy if the amplitude is doubled in a harmonic oscillator?

Answer: Total energy quadruples. Energy is proportional to $A^2$, so doubling A increases E by $2^2 = 4$.

Flashcard 74: Calculate the mass if $v = 4$ m/s and $KE = 32$ J.

Answer: $m = 4$ kg. Solving $32 = \frac{1}{2}m(4)^2$ gives $m = 4$ kg.

Flashcard 75: What is the unit of total mechanical energy in the SI system?

Answer: Joule (J). Energy is measured in joules in the SI system.