Establish the differential equation for simple harmonic motion (SHM) in one dimension. Show that for SHM, the velocity and acceleration of the particle is proportional to and
respectively, where
is the angular frequency of the particle.
### Establishing the Differential Equation for Simple Harmonic Motion (SHM) In one-dimensional simple harmonic motion, a particle moves under the influence of a restoring force that is proportional to its displacement from the equilibrium position and acts in the opposite direction. This force is given by Hooke’s Law: \[ F = -k x \] where: - \( F \) is the restoring force, - \( ________ _____ _________ _________ ______ _______ __________ _________ _________ ________ _____.
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The intensity ratio of two waves of same frequency and travelling in the same direction is 1:16. Calculate the ratio of their amplitudes.
Establish the differential equation for simple harmonic motion (SHM) in one dimension. Show that for SHM, the velocity and acceleration of the particle is proportional to and
respectively, where
is the angular frequency of the particle.
Standing waves are produced by the superposition of the following two waves:
y1 (x, t) = 0.2 sin (t - 2) and t2 (x,t) = 0.2 sin
(t+ 2x)
a) Obtain the resultant displacement of the particle at x at time t.
b) Calculate the value(s) of x for which displacement is zero.
c) Calculate the difference between two nearest values of x for which the displacement is zero. Is it related to the wavelength?
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.
What do you understand by wave impendence? Derive an expression for the impedance offered to sound waves propagating in a gaseous medium.
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.