14.16 Answer the following questions :

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

T = 2 $\mathit{\pi }\sqrt{\frac{\mathit{m}}{\mathit{k}}}\mathit{}.\mathit{}$ A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?

(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than 2 $\mathit{\pi }\sqrt{\frac{\mathit{l}}{\mathit{g}}}$ . Think of a qualitative argument to appreciate this result.

(c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall ?

 

(d) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

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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