The Period of a Conical Pendulum in Terms of Its Length (l), Semivertical Angle (θ) and Acceleration Due to Gravity (g) Is: - Physics


The period of a conical pendulum in terms of its length (l), semi-vertical angle (θ) and acceleration due to gravity (g) is:


  • `1/(2pi)sqrt((l costheta)/g)`

  • `1/(2pi)sqrt((l sintheta)/g)`

  • `4pisqrt((lcostheta)/(4g))`

  • `4pisqrt((l tantheta)/g)`



The time period of a conical pendulum is


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2014-2015 (March)


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If the metal bob of a simple pendulum is replaced by a wooden bob of the same size, then its time period will.....................

  1. increase
  2. remain same
  3. decrease
  4. first increase and then decrease.

When the length of a simple pendulum is decreased by 20 cm, the period changes by 10%. Find the original length of the pendulum.

The phase difference between displacement and acceleration of a particle performing S.H.M. is _______.

(A) `pi/2rad`

(B) π rad

(C) 2π rad


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

A simple pendulum of length and having a bob of mass is suspended in a car. The car is moving on a circular track of radius 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?

A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x0 and pushed towards the centre with a velocity v0 at time = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, x0 and v0. [Hint: Start with the equation acos (ωt) and note that the initial velocity is negative.]

A clock regulated by seconds pendulum, keeps correct time. During summer, length of pendulum increases to 1.005 m. How much will the clock gain or loose in one day?

(g = 9.8 m/s2 and π = 3.142)

Define practical simple pendulum

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.

If the particle starts its motion from mean position, the phase difference between displacement and acceleration is ______.

A simple pendulum has a time period of T1 when on the earth's surface and T2 when taken to a height R above the earth's surface, where R is the radius of the earth. The value of `"T"_2 // "T"_1` is ______. 

If the maximum velocity and acceleration of a particle executing SHM are equal in magnitude, the time period will be ______.

The period of oscillation of a simple pendulum of constant length at the surface of the earth is T. Its time period inside mine will be ______.

A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2. The period of oscillation is ______.

When will the motion of a simple pendulum be simple harmonic?

Find the time period of mass M when displaced from its equilibrium position and then released for the system shown in figure.

A body of mass m is situated in a potential field U(x) = U0 (1 – cos αx) when U0 and α are constants. Find the time period of small oscillations.

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.

A simple pendulum of time period 1s and length l is hung from a fixed support at O, such that the bob is at a distance H vertically above A on the ground (Figure). The amplitude is θ0. The string snaps at θ = θ0/2. Find the time taken by the bob to hit the ground. Also find distance from A where bob hits the ground. Assume θo to be small so that sin θo = θo and cos θo = 1.

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)


A particle at the end of a spring executes simple harmonic motion with a period t1, while the corresponding period for another spring is t2. If the period of oscillation with the two springs in series is T, then ______.


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