September 2025 - Page 33 of 101

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.

Introduction In this problem, we are given the equation of a sinusoidal wave in the form: y(x, t) = 3.0 sin(3.52t − 2.01x) (in cm) This standard wave equation allows us to extract different parameters of wave motion like amplitude, wave number, wavelength, angular frequency, and wave speed. Step-by-Step Extraction of Parameters 1. Amplitude (A) […]

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. Read More »

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.

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Introduction In this problem, we are given the oscillations at two different points on a wave. By analyzing the phase difference and distance between these points, we can determine the wavelength and speed of the wave. This is a typical problem related to wave propagation and phase relationships. Given y₁ = 0.3 sin(4πt) at x

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. Read More »

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.

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Introduction A forced oscillator is one that is subjected to a periodic external force. When damping is small, it is called a weakly damped forced oscillator. This system shows interesting behavior such as resonance and steady-state oscillation. In this question, we derive the equation of motion and interpret its terms. We also distinguish between the

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. Read More »

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.

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Introduction This is a damped harmonic oscillator problem where we need to calculate multiple physical parameters based on the values of mass, damping constant, and spring constant. The motion is governed by the differential equation: m d²x/dt² + γ dx/dt + kx = 0 Given: m = 0.50 kg γ = 0.70 kg/s k =

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. Read More »

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.

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Introduction We are given two harmonic oscillations: x₁ = 8 sin(100πt) x₂ = 12 sin(96πt) These are sinusoidal functions with different frequencies. When superposed, they result in a phenomenon known as beats. The amplitude of the resultant wave varies with time due to interference between the two waves. Step 1: Beat Frequency Let the two

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. Read More »

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?

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Introduction A seconds pendulum is defined as a simple pendulum whose time period is exactly 2 seconds. In this question, we calculate its length, angular frequency, and frequency. Additionally, we differentiate between a simple and compound pendulum. Given Time period (T) = 2 s Acceleration due to gravity (g) = 9.8 m/s² Step 1: Calculate

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? Read More »

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.

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Introduction Simple harmonic motion (SHM) is a type of oscillatory motion in which the restoring force is directly proportional to the displacement and acts in the opposite direction. The motion is sinusoidal in time and exhibits characteristics such as constant amplitude and periodicity. Displacement Equation Given the equation of SHM: x(t) = a cos(ωt) where:

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. Read More »

BPHE-101: Elementary Mechanics – All Assignment Answers (2025-26)

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BPHE-101: Elementary Mechanics – Assignment Answers (2025-26) Below is the complete list of answers for the IGNOU BPHE-101/PHE-01 Elementary Mechanics assignment for the 2025-26 session. Click on each question to read the detailed solution. A crate of mass 30.0 kg is pulled by a force of 300 N up an inclined plane… A ball having

BPHE-101: Elementary Mechanics – All Assignment Answers (2025-26) Read More »

b) A ball of mass 60g is moving due south with a speed of 50 ms⁻¹ at latitude 30ºN. Calculate the magnitude and direction of the coriolis force on the ball.

a) What should be the angular velocity of the earth such that a person of mass 80 kg standing on the earth at the equator would actually fly off the earth? b) A ball of mass 60g is moving due south with a speed of 50 ms⁻¹ at latitude 30ºN. Calculate the magnitude and direction of the coriolis force on the ball.