The figure shows the potential energy of a harmonic oscillator. Calculate: 1. Th

Question

The figure shows the potential energy of a harmonic oscillator. Calculate: 1. The number of one-minute oscillations. 2. The position of the oscillator at t = 2ns. 3. The mass of the particle. 4. The force on the particle if x = a / 4. 5. The force constant. The figure shows the potential energy of a harmonic oscillator. Calculate: 1. The number of one-minute oscillations. 2. The position of the oscillator at t = 2ns. 3. The mass of the particle. 4. The force on the particle if x = a / 4. 5. The force constant. U(x) A 5Lum 20km/s

Explanation / Answer

5. Total energy at x=a will only be due to the potential energy, then E = 1/2 k a2 => k=2E/a2 = 105 N/m

4. Force on the particle if x=a/4 => F = -Kx = -105 × a /4 = -0.125N

3. Total energy at x=0 will be due to the kinetic energy, then E = 1/2 m vm2 => m = 2E/vm2 = 6.25×10-15 kg

1. Time period of oscilllation = 2 (m/k) = 1.57×10-9 s = 1.57ns

    Number of oscillations in oneminute will be N = 60/ = 3.82×1010 .

2. Considering the time starts when the object is at postion x=0, equation of the postion of oscillator at time t

      x=a sin(t (k/m)) = 4.95×10-6 m

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