Two waves, travelling along the same direction, are given by
y1(x, t) = asin (ω1t − k1x)
and y2 (x, t) = asin (ω2t − k2x)
Suppose that the values of ω1 and k1 are respectively slightly greater than ω2 and
k2 . i) Obtain an expression for the resultant wave due to their superposition. ii)
Explain the formation of wave packet.
__________ _____ ________ ________ __________.
_________ ________ __________ ___ ____ ____.
________ _________ ________ _____ ____.
__________ ______ ___ ______ _________ ____ ________ _____ ____.
____ _________ ________ ___ ______ ______ ________ _______ _______ ____ ____.
______ ____ __________ __________ ________ ___ _____ ________ ______ _________ ___ ______.
__________ __________ ___ ______ __________ _________ _____ _____ ___ _____ ___.
______ __________ ____ _________ _________ ___ ______ ____ ___ ___.
_________ ____ ______ _________ ____ ___ ________ __________ _______ __________ _________ ___.
_______ ___ _____ ______ __________ _____ _______ ____ ________ ______ _________.
______ ______ _________ _______ ___ _________ ________ _______ ____.
_____ __________ ______ __________ _______ ___ _______ _________ _________ ________.
_________ ____ _______ ___ _______ _____ __________ _____ ______ __________ _________.
_______ ________ ___ ___ ____ _________ ______ _____ _________ ______ ____.
________ _____ _______ _____ ____ __________ ______ ___ __________ _______.
____ ______ _______ ________ _____ _____ ______ _________ ________ ______ __________.
________ _________ __________ ______ _____ ___ _____.
_________ _________ ___ ________ _______ _______ _______ ____ _________ ______ _____ __________.
_____ ___ ___ ___ _______ _____ ________ _______.
____ __________ _________ ______ ____ ________ ______ ________.
__________ __________ _______ ________ _________ _______ _____.
_____ ________ _________ ____ __________ _______ ____ ____ ______ ______ __________.
________ __________ _________ ____ _______ _______ _____.
________ __________ ____ __________ _______ ___ ______ __________ ______ __________.
_____ ________ __________ ______ ___ __________ ____ ________ ________.
__________ __________ ______ _________ _______ _______ _________.
__________ _________ _____ ________ ______ ____.
____ ___ ______ ___ _____ _________ _______ ________ _______ ________ ______.
__________ _______ ________ _____ _____ ________ ________ ______ ____ _______.
____ ______ ___ _____ _____ ____ ______.
______ __________ _________ _________ ___ ______ _________ ___ _____ ________ _________ ________.
__________ __________ ______ ____ _______ __________ _____ ___ ______ _____ _________ ____.
_________ __________ __________ ___ ____ ___ _______ ______ __________ _____.
_______ ____ _________ __________ ________ ________ ___ _______ ________.
__________ _________ __________ _____ ____ ________ _____ _______.
______ ______ _____.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
The amplitude of an oscillator is 8 cm and it completes 100 oscillations in 80s.
i) Calculate its time period and angular frequency. ii) If the initial phase is π/4, write expressions for its displacement and velocity. iii) Calculate the values of maximum
velocity and acceleration
Two waves, travelling along the same direction, are given by
y1(x, t) = asin (ω1t − k1x)
and y2 (x, t) = asin (ω2t − k2x)
Suppose that the values of ω1 and k1 are respectively slightly greater than ω2 and
k2 . i) Obtain an expression for the resultant wave due to their superposition. ii)
Explain the formation of wave packet.
Giving the necessary mathematical expressions, discuss the transient and steady state of a weakly damped forced oscillator. Show that the average power absorbed by a forced oscillator is given by
The equation of motion of a damped harmonic oscillator is given by
with m = 0.25 kg, b = 0.14 s −1
and ω0 = 18.4 s −1.
Calculate i) the time period; ii) number of oscillations in which its amplitude will become half of its initial value; and iii) number of oscillations in which its
mechanical energy will reduce to half of its initial value.
A body of mass 0.15 kg executes SHM described by the equation
x(t ) = 2 sin(πt + π / 4)
where x is in meters and t is in seconds.
i) Determine the amplitude and time period of the oscillation.
ii) Calculate the initial values of displacement and velocity.
iii) Calculate the values of time when the energy of the oscillator is purely kinetic.
An ambulance siren has frequency 250 Hz. The ambulance is headed towards an
accident site with a speed of 90 km h−1, Two police officers on separate motor
cycles head for the same accident site: one follows the ambulance with a speed of
80 km h−1 and the other approaches the accident site from the other direction with a
speed of 80 km h−1. What frequency does ambulance siren has for each of the police
officers? Take the speed of sound equal to 340 ms−1.
What is the effect of damping in an oscillatory system? Differentiate between heavy and critical damping. Show that the displacement of a weakly damped oscillator is given by
x(t ) = a0 exp(−bt ) cos(ωd t − φ)
where symbols have their usual meanings.