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