1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculate total mechanical energy of a frictionless spring

  1. Feb 22, 2016 #1
    Could you please help me determine if I've worked this problem out correctly.

    1. The problem statement, all variables and given/known data

    A 2.86-kg object on a frictionless horizontal surface oscillates at the end of a spring with an amplitude of
    7.81 cm. Its maximum acceleration is 3.74 m/s2.
    Calculate the total mechanical energy.

    2. Relevant equations

    1) Total Mechanical Energy: E = 0.5 k A^2
    2) Spring Constant: k = m w^2 (where w = angular velocity)
    3) Acceleration : a = -w^2 x

    3. The attempt at a solution

    Given the Amplitude A, we must calculate the spring constant k to calc the total mechanical energy.

    First find w using formula 3)
    w = - sqr( a / x)
    w = - sqr(3.74 / 0.0781)
    w = - 6.92

    Now substitute k in formula 1 with formula 2 to calculate the total mechanical energy.

    E = 0.5 (m w^2) A^2
    E= 0.5 (2.86) (-6.92)^2 (0.0781)^2
    E= 0.0418 Joules
  2. jcsd
  3. Feb 22, 2016 #2


    User Avatar

    Staff: Mentor

    Your method is fine.

    Re-do your final calculation; you seem to have slipped a decimal point.
  4. Feb 22, 2016 #3
    Yes it's okay but pay attention at this:

    a= -ω^2 x ---> ω= √(-a/x)

    Since a is opposite to x a= -3.74 m/s^2 and ω= 6.92 rad/s so ω>0
  5. Feb 22, 2016 #4
    Thank you for the feedback and for checking my shoddy calculation.

    I redid the calculation and the answer came to 0.418 Joules
  6. Feb 22, 2016 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You mean, so ω is real. Whether you choose to take the positive or negative root is another matter.
  7. Feb 22, 2016 #6
    Yes, I just focused on the fact that he got a ω< 0 by making a little mistake in solving a= -ω^2 x

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Calculate total mechanical energy of a frictionless spring
  1. Total mechanical energy (Replies: 15)