Question

3.
A 2 kg body panel of a car oscillates with a frequency of 2 Hz and amplitude 2.5 cm. If the
oscillations are assumed to be simple harmonic and undamped, calculate

(a) the total energy of the panel
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Answer 1

Answer:

Explanation:

Energy in simple harmonic motion

The kinetic energy of any body of mass m is given by kinetic energy = ½ mv2

So, in simple harmonic motion:

Kinetic energy = ½ mω2(r2 - x2)

Now the maximum value of the kinetic energy will occur when x = 0, and this will be equal to the total energy of the body. Therefore:

Total energy = ½ mω2r2

Therefore, since:

potential energy = total energy – kinetic energy, the potential energy at any point will be given by:

Potential energy = ½ mω2x2