Question

A particle of mass 0.5 kg executing simple harmonic motion of amplitude 5cm has a maximum speed of 31.4 cm/s. The total energy of the oscillator is:

• A. 24.6 J
• B. 0.0246 J
• C. 246 J
• D. 2.46 J

Answer 1

Answer: (B)

0.0246 J

Answer 2

The total energy of a particle executing simple harmonic motion (SHM) is constant and can be expressed as:

$E = \frac{1}{2} m v_{max}^2$

where:

$m$ is the mass of the particle $v_{max}$ is the maximum speed of the particle

Given values: $m = 0.5 \, \text{kg}$ $v_{max} = 31.4 \, \text{cm/s} = 0.314 \, \text{m/s}$

$E = \frac{1}{2} \times 0.5 \, \text{kg} \times (0.314 \, \text{m/s})^2 = 0.0246 \, \text{J}$