BPHE-102: Oscillations and Waves – All Questions Answered
Below are the complete answers to the IGNOU assignment for BPHE-102: Oscillations and Waves (2025). Click on each question to view its detailed solution.
- a) A simple harmonic motion is represented by x(t) = a cos(ωt). Obtain expressions for velocity and acceleration of the oscillator. Also, plot the time variation of displacement, velocity and acceleration of the oscillator.
- b) The time period of a simple pendulum, called ‘seconds pendulum’, is 2 s. Calculate the length, angular frequency and frequency of the pendulum. What is the difference between a simple pendulum and a compound pendulum?
- c) Two collinear harmonic oscillations x₁ = 8 sin (100πt) and x₂ = 12 sin (96πt) are superposed. Calculate the values of time when the amplitude of the resultant oscillation will be (i) maximum and (ii) minimum.
- d) For a damped harmonic oscillator, the equation of motion is m d²x/dt² + γ dx/dt + kx = 0 with m = 0.50 kg, γ = 0.70 kg/s and k = 70 N/m. Calculate (i) the period of motion, (ii) number of oscillations in which its amplitude will become half of its initial value, (iii) the number of oscillations in which its mechanical energy will drop to half of its initial value, (iv) its relaxation time, and (v) quality factor.
- e) Establish the equation of motion of a weakly damped forced oscillator explaining the significance of each term. Differentiate between transient and steady state of the oscillator.
- a) The oscillations of two points x₁ and x₂ at x = 0 and x = 1 m respectively are modelled as: y₁ = 0.3 sin(4πt) and y₂ = 0.3 sin(4πt + π/8). Calculate the wavelength and speed of the associated wave.
- b) A sinusoidal wave is described by y(x, t) = 3.0 sin(3.52t − 2.01x) cm. Determine the amplitude, wave number, wavelength, frequency and velocity of the wave.
- c) The linear density of a vibrating string is 1.3 × 10⁻⁴ kg/m. A transverse wave is propagating on the string and is described by the equation y(x, t) = 0.021 sin(30t − x). Calculate the tension in the string.
- d) A stretched string of mass 20 g vibrates with a frequency of 30 Hz in its fundamental mode and the supports are 40 cm apart. The amplitude of vibrations at the antinode is 4 cm. Calculate the velocity of propagation of the wave in the string as well as the tension in it.
- e) Consider two cylindrical pipes of equal length. One of these acts as a closed organ pipe and the other as open organ pipe. The frequency of the third harmonic in the closed pipe is 200 Hz higher than the first harmonic of the open pipe. Calculate the fundamental frequency of the closed pipe.
Course Code: BPHE-102
Course Title: Oscillations and Waves
Assignment Code: BPHE-102/PHE-02/TMA/2025
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