why is the minimum velocity of a a simple pendulum in verticle circular motion at top under root gl

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Q. (a) Define simple harmonic motion. Show that the motion of (point) projection of a particle performing uniform circular motion, on any diameter, is simple harmonic.
(b) Can a simple pendulum be used in an artificial satellite? Give the reason

Q. A simple pendulum of mass m is performing vertical circular motion with its velocity at the highest point being V

= \sqrt{2 g l}

where l is the length of the string. Find the tension in the string when it reaches the lowest point.

Q. The simple pendulum bob is given a horizontal velocity

\sqrt{g l}

at the bottom. The angle with the vertical through which the ball swings before its velocity becomes zero is

Q. Assertion :For an oscillating simple pendulum, the tension in the string is maximum at the mean position and minimum at the extreme position. Reason: The velocity of the oscillating bob in simple harmonic motion is maximum at the mean position.

Answer the following questions:

(a) 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?

(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. 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 cabinthat is freely falling under gravity?

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