4

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):

(a) sin ωt – cos ωt

(c) 3 cos (π/4 – 2ωt)

(d) cos ωt + cos 3ωt + cos 5ωt

(e) exp (–ω^{2}t^{2})

(f) 1 + ωt + ω^{2}t^{2}

7

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

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.

16

Answer the following questions:

Time period of a particle in SHM depends on the force constant k and mass m of the particle:

. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?