VIB - Energy in Simple Harmonic Motion

Energy in Simple Harmonic Motion

Conservation of energy can be used to determine the position and velocity of a particle that is undergoing simple harmonic motion. The total energy of the system depends on the elastic constant and the amplitude of motion. For values of kinetic and potential energy at exact time periods, we use the equations for position and velocity discussed in the first section of this module. For potential energy, we use the equation for position as a function of time. For kinetic energy, we use the equation for the velocity as a function of time. Please watch the following presentation that will discuss energy as it relates to objects undergoing simple harmonic motion.

Energy in Simple Harmonic Motion Practice

We will now practice solving problems using the concepts you learned in the presentation. Make sure to show all your work when solving problems. The presentation will give you time to work through the problems, find a solution, and check your work. 

Energy in Simple Harmonic Motion Self-Assessment

Now it's your turn. Complete the self-assessment questions to verify that you can apply energy considerations to objects undergoing Simple Harmonic Motion.

  1. A 0.200 kg block is suspended vertically from a spring. When an additional 0.100 kg is placed on the spring it stretches an additional 3 cm. With both masses on the spring, it is allowed to oscillate with an amplitude of 7cm.  
    1. What is the frequency of the motion?
    2. How long does it take the blocks to move from their highest point to their lowest point?
    3. What is the maximum force applied to the combined 0.300kg mass?
    4. What is the maximum speed that the blocks attain?

SOLUTIONS Links to an external site.

  1. An object with a mass of m is suspended from a vertical spring with a constant of 1,500 N/m. The object is pulled down 6.5 cm from equilibrium and released with no initial kinetic energy. The mass is observed to oscillate with a period of 0.20s.
    1. Find m.
    2. Find how much the spring is stretched when it has the mass hanging from it, but is not in motion.
    3. Write the equation for the position of the spring as a function of time. 

SOLUTIONS Links to an external site.

  1. A particle with a mass of 0.25 kg undergoes Simple Harmonic Motion. The position of the particle as a function of time is given by the equation LaTeX: x\left(t\right)=0.33\cos\left(11t+0.18\right)x(t)=0.33cos(11t+0.18) .
    1. What is the potential energy of the particle at t=2.5s?
    2. What is the kinetic energy of the particle at this time?

SOLUTIONS Links to an external site.

Energy in Simple Harmonic Motion Practice Problems

Download Energy in Simple Harmonic Motion Practice Problems Links to an external site. for more practice. 

Download solutions Links to an external site. to the practice problems. 

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