The total mechanical energy of a harmonic oscillator that consists of a spring w

Question

The total mechanical energy of a harmonic oscillator that consists of a spring with spring constant k and mass m is E subscript t o t end subscript equals 1 half m v squared plus 1 half k x squared Here K equals 1 half m v squared is the kinetic energy of the mass and U subscript e l end subscript equals 1 half k x squared is the elastic potential energy of the spring. If there are no other dissipative forces acting (e.g. friction or airdrag are negligible), the total mechanical energy is conserved. This means the oscillator reaches maximum displacement xmax=A (amplitude) for v=0, and maximum speed vmax for x=0.

Consider a harmonic oscillator with mass 0.2 kg and spring constant 181 N/m. If the speed of the mass at the equilibrium point is 1.1 m/s, what is the amplitude? (work this out using conservation of energy. Practise how to draw an energy bar chart for this.) Convert your answer to units of cm.

Explanation / Answer

we know that 0.5mv2 =kx

x = 0.5*0.2*1.12/181 = 6.685 x 10^-4 m

or 0.0668 cm........Ans.

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