Question

3. What is the time period of a simple harmonic pendulum kept in a freely falling lift? Explain.
The displacement of a particle varies with time according to the relation x= 4(cos πt + sin πt)
cm. Show that the motion of the particle is simple harmonic and its amplitude is 4√2.

Answer 1

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PHYSICS

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=2πkm. 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 angle of oscillation a more involved analysis shows that T is greater than 2πgl. 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 ?

November 22, 2019Mathan Jivani

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ANSWER

(a) For a simple pendulum, force constant or spring factor k is proportional to mass m, therefore, m cancels out in denominator as well as in numerator. That is why the time period of simple pendulum is independent of the mass of the bob.

(b) In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is given as:

F=–mgsinθ

where,

F= Restoring force

m= Mass of the bob

g= Acceleration due to gravity

θ= Angle of displacement

For small θ,sinθ≃θ

For large θ, sinθ is greater than θ.

This decreases the effective value of g.

Hence, the time period increases as:

T=2πgl

(c) Yes, because the working of the wrist watch depends on spring action and it has nothing to do with gravity.

(d) Gravity disappears for a object under free fall, so frequency is zero.