Simple Harmonic Motion and Uniform Circular Motion

The motion of a particle executing simple harmonic motion is described by the displacement function,

x (t) = A cos (ωt + φ).

If the initial (t = 0) position of the particle is 1 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^–1. If instead of the cosine function, we choose the sine function to describe the SHM: x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.

Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is ______.

A particle is in linear simple harmonic motion between two points A and B, 10 cm apart (Figure). Take the direction from A to B as the + ve direction and choose the correct statements.

1. The sign of velocity, acceleration and force on the particle when it is 3 cm away from A going towards B are positive.
2. The sign of velocity of the particle at C going towards O is negative.
3. The sign of velocity, acceleration and force on the particle when it is 4 cm away from B going towards A are negative.
4. The sign of acceleration and force on the particle when it is at point B is negative.

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 ωt – cos ωt

The rotation of earth about its axis is ______.

1. periodic motion.
2. simple harmonic motion.
3. periodic but not simple harmonic motion.
4. non-periodic motion.

A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ωt and y = a sin ωt. The trajectory of motion of the particle will be ______.

In figure, what will be the sign of the velocity of the point P′, which is the projection of the velocity of the reference particle P . P is moving in a circle of radius R in anticlockwise direction.

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):

exp (–ω²t²)