14.4 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 ( $\mathit{\omega }$ is any positive constant):

(a) Sin $\mathit{\omega }$ t – cos $\mathit{\omega }$ t

(b) Sin³ $\mathit{\omega }$ t

(c) 3 cos ( $\mathit{\pi }$ /4 – 2 $\mathit{\omega }$ t)

(d) Cos $\mathit{\omega }$ t + cos 3 $\mathit{}\mathit{\omega }$ t + cos 5 $\mathit{}\mathit{\omega }$ t

(e) Exp (– $\mathit{\omega }$ 2t2)

(f) 1 + $\mathit{\omega }$ t + $\mathit{\omega }$ ²t²

If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. New amplitude of oscillation will be:

The fundamental frequency of an organ pipe open at one end is 300 Hz. The frequency of 3rd overtone of n Find n.×this organ pipe is 100 Hz

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is T_b / T_a = √x, where value of x is ................... (Round off to the Nearest Integer)

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->