1A) The total mechanical energy of a harmonic oscillator that consists of a spri
ID: 1473500 • Letter: 1
Question
1A) The total mechanical energy of a harmonic oscillator that consists of a spring with spring constant k and mass m is
Consider a harmonic oscillator with mass 0.26 kg and spring constant 181 N/m. If the speed of the mass at the equilibrium point is 1.88 m/s, what is the amplitude? (work this out using conservation of energy. Practise how to draw an energy bar chart for this.)
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1B) Consider a harmonic oscillator with mass 0.34 kg and spring constant 199 N/m. If the amplitude is 7.74 cm, what is the speed of the mass at the equilibrium point? (work this out using conservation of energy. Practise how to draw an energy bar chart for this.)
Explanation / Answer
total energy od sysrtem will be same at every positiion.
Total energy = PE + KE
Total energy at equilibrium = at extreme point
0 + mv^2 /2 = kA^2 /2 + 0
0.26 x 1.88^2 = 181A^2
A =0.0713 m
Amplitude = 0.0713 m = 7.13 cm
1B) again using energy conservation,
m * v_max^2 /2 = k A^2 /2
0.34 * v^2 = 199 (0.0774)^2
v = 1.87 m/s
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