a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion) ? Fig.
. . Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ( ω is any positive constant): sin ω t – cos ω t sin ω t cos ( π / – ω t ) (d) cos ω t + cos ω t + cos ω t (e) exp (– ω t ) (f) + ω t + ω t .
A particle is in linear simple harmonic motion between two points, A and B, cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the end A, at the end B, at the mid-point of AB going towards A, (d) at cm away from B going towards A, (e) at cm away from A going towards B, and (f) at cm away from B going towards A. . Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?
a = . x a = – x a = – x (d) a = x . The motion of a particle executing simple harmonic motion is described by the displacement function, x ( t ) = A cos ( ω t + φ ). If the initial ( t = ) position of the particle is cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle ?
The angular frequency of the particle is π s – . If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin ( ω t + α ), what are the amplitude and initial phase of the particle