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# 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)

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

### 1 Answer

- civil_av8rLv 74 years agoFavorite Answer
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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