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

x(t) = A cos ( $\mathit{\omega }$ t + $\mathit{\phi }$ ).

If the initial (t = 0) position of the particle is 1 cm and its initial velocity is $\mathit{\omega }\mathit{}$ cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is $\mathit{\pi }$ s^–1. If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin ( $\mathit{\omega }$ t + $\mathit{\alpha }$ ), what are the amplitude and initial phase of the particle with the above initial conditions.

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?
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