The weight on a vertical spring undergoes forced vibrations according to the following equation:
where x is the displacement from the equilibrium position and > 0 is a constant. If at t = 0, x = 0 and
calculate x as a function of t.
The given second-order differential equation is: \[ \frac{d^{2}x}{dt^{2}} + 4x = 8\sin(\omega t) \] with initial conditions: \[ x(0) = _________ ________ ___ _______ ________.
________ ___ _____ _____ _________ ________ ____ ______ _________ ____.
______ ________ _____ ______ __________ _____ _______ ___.
________ ___ ___ _______ _____ ___ __________.
________ ____ __________ ___ ______ ________ ____ ______ _______ __________ ____ __________.
___ ________ ______ ____ _________ ______.
_______ ____ _____ ________ ____ __________ ______ ______ _______ ______.
_____ __________ _________ ______ ___.
_______ __________ __________ _________ ________ _____ _________ ______.
_________ _____ ______ ________ _________ __________ _______ ________ _________ _____.
_______ _________ __________ __________ ____.
______ _________ _____ __________ _______ ___ ___ _____ ____ _______.
_______ _____ _____ _________ _________.
_____ ___.
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The displacement of an object executing SHM is given by:
x = 0.02 cos 4 (t + 0.625)m
Calculate the amplitude, period, maximum velocity, maximum acceleration and initial displacement of the object.
i) Two collinear SHMs of amplitudes 3 and 4 units add up to an SHM of amplitude units. Calculate the phase difference between the two superposing SHMs.
ii) A particle is simultaneously subjected to two mutually perpendicular oscillations given by
x = 3 sin cm, y = 3 cos
cm Determine its trajectory of motion.
What do you understand by wave impendence? Derive an expression for the impedance offered to sound waves propagating in a gaseous medium.
The natural angular frequency of an oscillator is 0. It is subjected to a damping force proportional to velocity and the damping force per unit mass per unit velocity is b. A periodic force given by F cos t is applied to it. Establish the differential equation for the oscillator and obtain the condition for velocity resonance.
Two waves are represented by:
y = a sin and y = b cos
Calculate the phase difference between the waves.
Calculate the fundamental frequency and the first 3 overtones of a pipe of length 1.7 m and closed at one end.
A wave is expressed as: y = 0.5 sin (0.01x - 3t) Calculate the speed of propagation of the wave.