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A Time Period of a Particle in Shm Depends on the Force Constant K And Mass M Of the Particle: `T = 2pi Sqrt(M/K)` A Simple Pendulum Executes Shm Approximately. Why Then is the Time

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प्रश्न

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 = 2pi sqrt(m/k)` A simple pendulum executes SHM approximately. Why then is the time 

 

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उत्तर १

The time period of a simple pendulum, `T = 2pi sqrt(m/k)`

For a simple pendulum, k is expressed in terms of mass m, as: `k prop m` 

`m/k =` Constant

Hence, the time period T, of a simple pendulum is independent of the mass of the bob.

 

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उत्तर २

In case of a spring, k does not depend upon m. However, in case of a simple pendulum, k is directly proportional to m and hence the ratio m/k is constant quantity

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 13: Oscillations - Exercises [पृष्ठ ३६०]

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एनसीईआरटी Physics Part 1 and 2 [English] Class 11
पाठ 13 Oscillations
Exercises | Q 16.1 | पृष्ठ ३६०

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

let us take the position of mass when the spring is unstretched as x = 0, and the direction from left to right as the positive direction of the x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is

(a) at the mean position,

(b) at the maximum stretched position, and

(c) at the maximum compressed position.

In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?


The acceleration due to gravity on the surface of moon is 1.7 ms–2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 ms–2)


Answer the following questions:

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 `2pisqrt(1/g)`  Think of a qualitative argument to appreciate this result.


Answer the following questions:

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?


Answer the following questions:

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


A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?


The cylindrical piece of the cork of density of base area A and height h floats in a liquid of density `rho_1`. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period

`T = 2pi sqrt((hrho)/(rho_1g)` 

where ρ is the density of cork. (Ignore damping due to viscosity of the liquid).


Show that motion of bob of the pendulum with small amplitude is linear S.H.M. Hence obtain an expression for its period. What are the factors on which its period depends?


Show that, under certain conditions, simple pendulum performs the linear simple harmonic motion.


The relation between acceleration and displacement of four particles are given below: Which one of the particles is executing simple harmonic motion?


Two identical springs of spring constant K are attached to a block of mass m and to fixed supports as shown in figure. When the mass is displaced from equilibrium position by a distance x towards right, find the restoring force


Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of 2° to the right with the vertical, the other pendulum makes an angle of 1° to the left of the vertical. What is the phase difference between the pendulums?


A tunnel is dug through the centre of the Earth. Show that a body of mass ‘m’ when dropped from rest from one end of the tunnel will execute simple harmonic motion.


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. The new amplitude of oscillation will be:


A pendulum of mass m and length ℓ is suspended from the ceiling of a trolley which has a constant acceleration a in the horizontal direction as shown in the figure. Work done by the tension is ______.

(In the frame of the trolley)

 


If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is `x/2` times its original time period. Then the value of x is ______.


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