Energy of Simple Harmonic Oscillators Practice

Sample questions

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1. Sample 1difficulty 1/5

   In a spring-mass SHM, kinetic energy is maximum

   • A

     At equilibrium (x = 0)

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   • B

     Halfway between

   • C

     Everywhere the same

   • D

     At the extremes (x = ±A)

   Why

   At equilibrium, all energy is kinetic ($U = 0$), so $K$ is at its maximum.

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2. Sample 2difficulty 2/5

   The graph shows kinetic energy $K$, potential energy $U$, and total energy $E$ as functions of position for an ideal spring oscillator with amplitude $A$. At $x = 0$ (equilibrium), how does $K$ compare to $U$?

   • A

     $K = E$, $U = 0$

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   • B

     $K = U = E/2$

   • C

     $K = 0$, $U = E$

   • D

     $K = E/2$, $U = E$

   Why

   At equilibrium the spring is unstretched, so $U = \tfrac{1}{2}k(0)^2 = 0$, and all the energy is kinetic: $K = E$.

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3. Sample 3difficulty 2/5

   A spring oscillator with $k = 100~\text{N/m}$ and amplitude $A = 0.20~\text{m}$ has total mechanical energy

   • A

     $1.0~\text{J}$

   • B

     $10~\text{J}$

   • C

     $4.0~\text{J}$

   • D

     $2.0~\text{J}$

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   Why

   $E = \tfrac{1}{2}k A^2 = \tfrac{1}{2}(100)(0.04) = 2.0~\text{J}$.

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4. Sample 4difficulty 2/5

   A spring-mass oscillator has $k = 80~\text{N/m}$ and amplitude $A = 0.20~\text{m}$. What is its total mechanical energy?

   • A

     $0.80~\text{J}$

   • B

     $1.6~\text{J}$

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   • C

     $16~\text{J}$

   • D

     $3.2~\text{J}$

   Why

   $E = \tfrac{1}{2}k A^2 = \tfrac{1}{2}(80)(0.20)^2 = 1.6~\text{J}$.

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5. Sample 5difficulty 2/5

   The shape of $U(x)$ for an ideal spring-mass oscillator is

   • A

     Constant

   • B

     Linear

   • C

     Parabolic

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   • D

     Hyperbolic

   Why

   $U = \tfrac{1}{2}k x^2$ is a parabola opening upward, symmetric about $x = 0$.

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