Anonymous
Anonymous asked in Science & MathematicsPhysics · 4 years ago

Energy in an Oscillating Spring?

A 1.15 kg mass on a spring oscillates horizontal frictionless surface. The motion of the mass is described by the equation: x = 0.37cos(3.39t).

In the equation, x is measured in meters and t in seconds. What is the maximum energy stored in the spring during an oscillation?

(in J)

Update:

Please provide an explanation for your equations to help me learn! Thank you.

1 Answer

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  • 4 years ago
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    The natural frequency is 3.39 rad/s

    Then equation for natural freq of a spring-mass system

    w = sqrt (k/m)

    Solve for the spring constant

    K = m*w^2

    Max displacement (amplitude) occurs when the cos term = 1

    A = 0.37 m (assuming meters, you left off units)

    The max spring pe occurs at the max displacement

    SPE Max = 1/2*k*A^2 = 1/2*m*w^2*A^2

    All your numbers are known so now you just have to plug them in.

    Hope the explanation helped.

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